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electronics
Review
Massive MIMO Wireless Networks: An Overview
Noha Hassan †^ ID^ and Xavier Fernando *,†
Department of Electrical and Computer Engineering, Ryerson University, 350 Victoria Street,
* Correspondence: [email protected]; Tel.: +1-416-979-5000 (ext. 6077)
† These authors contributed equally to this work.
Received: 31 July 2017; Accepted: 26 August 2017; Published: 5 September 2017
Abstract: Massive multiple-input-multiple-output (MIMO) systems use few hundred antennas to
simultaneously serve large number of wireless broadband terminals. It has been incorporated
into standards like long term evolution (LTE) and IEEE802.11 (Wi-Fi). Basically, the more the
antennas, the better shall be the performance. Massive MIMO systems envision accurate beamforming
and decoding with simpler and possibly linear algorithms. However, efficient signal processing
techniques have to be used at both ends to overcome the signaling overhead complexity. There are
few fundamental issues about massive MIMO networks that need to be better understood before their
successful deployment. In this paper, we present a detailed review of massive MIMO homogeneous,
and heterogeneous systems, highlighting key system components, pros, cons, and research directions.
In addition, we emphasize the advantage of employing millimeter wave (mmWave) frequency in the
beamforming, and precoding operations in single, and multi-tier massive MIMO systems.
Keywords: 5G wireless networks; massive MIMO; linear precoding; encoding; channel estimation;
pilot contamination; beamforming; HetNets
1. Introduction
According to CISCO, an american multinational technology company, by 2020, more people
(5.4 B) will have mobile phones than have electricity (5.3 B), running water (3.5 B) and cars (2.8 B).
In addition, 75% of the mobile data traffic will be bandwidth-hungry video. Users will expect wireline
quality in wireless services and higher bit rates and more reliable connections will be mandatory. While
conventional techniques struggling to provide these bit rates, massive multiple-input-multiple-output
(MIMO) systems promise 10 s of Gbps data rates to support real-time wireless multimedia services
without occupying much additional spectrum [1].
Massive MIMO technology has got much attraction lately as it promises truly broadband wireless
networks [ 2 ]. Massive MIMO systems use base station (BS) antenna arrays, with few hundred
elements, simultaneously serving many tens of active terminals (users) using the same time and
frequency resources.
1.1. Background
It is well known that, in classical MIMO, multiple antennas at both ends exploit wireless channel
diversity to provide more reliable high-speed connections. Massive MIMO (also known as Large-Scale
Antenna Systems, Very Large MIMO, Hyper MIMO, and Full-Dimension MIMO) makes a bold
development from current practice using a very large number of service antennas (e.g., hundreds or
thousands) that are operated fully coherently and adaptively.
Figure 1 shows the speed improvement of wireless networks over the years starting from
single-input-single-output (SISO) systems, single user (SU) and multiple users (MU) MIMO networks.
MU-MIMO systems already provide significant advantages over earlier systems. Massive MIMO
Electronics 2017 , 6 , 63; doi:10.3390/electronics6030063 www.mdpi.com/journal/electronics
aims to further enhance this (to 10 Gbps and more) using hundreds of antennas exploiting advances
in parallel digital signal processing and high-speed electronics. Extra antennas help with focusing
the transmission and reception of signal energy into ever-smaller regions of space. This brings huge
improvements in throughput and energy efficiency, in particular when combined with simultaneous
scheduling of numerous user terminals (e.g., tens or hundreds).
Figure 1. Evolving speed of wireless networks.
The more the BS antennas used, the more the data streams can be released to serve more terminals,
reducing the radiated power, while boosting the data rate. This will also improve link reliability
through spatial diversity and, provide more degrees of freedom in the spatial domain, and improve the
performance irrespective of the noisiness of the measurements. In addition, because massive MIMO
systems have a broad range of states of freedom, and greater selectivity in transmitting and receiving
the data streams, interference cancellation is enhanced. BSs can relatively easily avert transmission into
undesired directions to alleviate harmful interference which, leads to low latency as well. In addition,
massive MIMO makes a proper use of beamforming techniques to reduce fading drops; this further
boosts signal-to-noise-ratio (SNR), bit rate and reduces latency [3].
Furthermore, increasing the number of BS antennas above the number of active users leads
to higher throughput [ 1 ]. Channel estimation quality per antenna also improves with the number
of BS antennas especially in the presence of high correlation among the antennas which is very
typical [ 4 ]. In addition, the eigenvalue histogram of a single implementation converges to the average
asymptotic eigenvalue distribution [ 5 ]. This leads to the possibility of employing simple low complexity
detection techniques while preserving an excellent performance. In addition, the channel becomes
more predestined and random detectors matrices are readily solved.
Aggressive spatial multiplexing in massive MIMO systems leads to an impressive improvement
in the network capacity by minimizing multiuser interference by steering the signal accurately in the
right direction. Massive MIMO systems concentrate the released energy into small user centric zones,
which dramatically increases the throughput and the energy efficiency [ 1 ]. Since all of the users can
take part in the multiplexing gain, costly antenna array deployments are only necessary on the BS side,
which saves on costs by sharing. This also leaves the user equipment less complex, often with a single
antenna. A higher number of BS antennas revokes the effects of uncorrelated noise and small-scale
fading, and lowers the required transmitted energy per bit [ 6 ]. The propagation medium minimally
affects the performance of a massive MIMO system because of multi-user diversity.
Due to the advantages and popularity of massive MIMO, recently there has been an increase in
papers written on this area. Table 1 describes some of these.
Table 2. Comparison between cooperating and non-cooperating multipl-input-multiple-output
(MIMO) systems.
Cooperating Systems (Networked MIMO)
Non-Cooperating Systems (Conventional Massive MIMO)
Multiple fold increase in spectral efficiency. Less.
Less energy consumption. Less energy saving.
Cooperation between BSs with small antenna arrays.
Noncooperation: Each BS is robust against ICI 1
More controls (yields in better performance). Fewer controls (yields in better implementation).
Less downlink user rate. Improvement in the downlink user rate.
Each user experiences less quality of service. More user quality of service.
Increased system complexity, and the large signaling overhead, which is reduced by distributed optimization.
Less Complexity.
Improved capacity, coverage, and cell edge throughput.
Improved capacity, coverage, and cell edge throughput.
1 Inter-Carrier Interference.
1.3. Massive MIMO in Wireless Sensor Networks
Wireless sensor networks (WSN) are special kinds of monitoring networks, aiming at detecting,
measuring, monitoring certain physical phenomena, such as temperature, humidity, pressure,
vibration, etc. Each device in the WSN is termed as a node that exchanges information with its
neighbour. Typically nodes have limited connectivity and energy resources. All data will be poured
into a BS node, or a sink, which in turn relays the information to an outside user, or a server to process
it. WSN nodes are small in size, cheap in cost, and do not employ complicated processing units, except
the sink node. WSN may be composed of hundreds or thousands of nodes to provide coverage on
a large scale basis.
Recently, several research efforts have been addressed to discuss the benefit of introducing
a massive number of antennas at the BS, or the sink node. Multiple antennas at the BS improve the
detection performance, the estimation performance, and energy efficiency, even when using simpler
algorithms, and linear receivers with partial CSI knowledge.
In [ 16 ], the authors studied the detection, and estimation performances of a Gaussian signal
communicating over a coherent multiple access channel in a WSN having a massive MIMO BS,
or fusion center (FC). The Neyman–Pearson detectors and the linear minimum mean squared error
(LMMSE) estimation detectors that require full CSI were studied. Significant performance gains were
achieved at low sensor transmit power levels. However, the energy detector shows improvement in
gain under both low and high sensor power assumptions.
In addition, in [ 17 ], the authors compared the performance of a low cost energy detector to that of
an expensive complex optimal detector, in a WSN having multiple antennas at the FC, both analytically
and by simulation.
Finally, the authors in [ 18 ] optimized the transmission power at each node of a WSN having
multiple antennas at the FC, using two different scenarios—in correlated and in uncorrelated fading
channels with noise. The authors proved that the total power consumption at the nodes is saved as the
number of antennas increases.
2. Homogeneous MIMO (Single Tier Systems)
Conventional MIMO systems are composed of randomly distributed multiple antenna BSs,
where each BS is serving a certain number of users. All BSs are working with the same access methods,
diversity techniques, and type of transmission. The average transmit power per unit service area is
also often the same (subjected to power control algorithms).
Figure 2 shows the uplink and the downlink of a massive MIMO single cell system. As shown in
Figure 2, the BS is composed of a few hundred service antennas serving a few hundred users each,
usually with only one antenna.
Figure 2. Uplink and downlink operation of a MIMO link.
The steps of the uplink operation are as follows [7]:
1. Encoding is employed to prepare data for transmission.
2. Pilot sequences and uplink data sequences are transmitted at the same time and over the same
frequencies from each user to the BS.
3. The BS receives the sum of data streams from all the users, and estimates the channel.
4. Decoding and detection operations produce individual data streams by utilizing the
estimated CSI.
The steps of the downlink process are as follows:
1. Beamforming: Data streams are transmitted from the BSs to only the intended users by means of
beamforming, where the different data streams may occupy the same frequencies at the same
time (space division multiplexing).
2. Precoding: The previous operation is carried out knowing the frequency response of the
propagation channels (or CSI) between each of its elements and each user and precoding the
signals accordingly.
Linear decoding or demultiplexing is employed on the uplink, while linear precoding or
multiplexing is employed on the downlink. Figure 3 shows major elements of a massive MIMO system.
Linear precoding techniques at the downlink aim to focus each signal at its desired terminal
and mitigate interference towards other terminals [ 1 ]. Meanwhile, receive combining is used in the
uplink for differentiation between signals sent from different terminals. The more the antennas used,
the finer the spatial focusing can be. Low-complexity precoding methods are mandatory and critical to
minimize the computational complexity of the precoder [19].
Unlike the conventional MIMO, massive MIMO uses linear precoders, such as maximum ratio
combining (MRC), matched filtering, conjugate beamforming, minimum mean squared error (MMSE)
receive combining, and zero-forcing (ZF) [4].
- Angle of Arrival (AOA) based methods: Use the fact that non-overlapping user terminals
reusing the pilots would have different AOA. However, this needs a way to detect AOA such as
directional antennas.
2.2. Encoding Techniques
MIMO encoding is all about converting data into symbols appropriate for transmission over
multiple transmit antennas. Space multiplexing and space-time coding are the commonly used
encoding techniques, as they do not require knowledge of the CSI at the transmitter. Table 3 compares
Spatial Multiplexing, Space–Time Coding, and Spatial Modulation. MIMO encoding using known CSI
at the transmitter is known as precoding [5].
Table 3. Comparison between spacial multiplexing, space-time coding, and spatial modulation.
Spacial Multiplexing Space–Time Coding Spatial Modulation
Achieves high rates. Achieves increased reliability through transmit diversity. Allows fewer transmit RF 1 chains.
Information is carried on the modulation symbols.
Information is carried on the modulation symbols.
Information is carried on the modulation symbols in addition to the indices of the antennas on which transmission takes place.
Simplest (only the receiver needs to detect transmitted symbols). Sophisticated.
Simple, but requires additional memory to construct encoding table at the transmitter.
Example: V-BLAST. Space–Time Trellis. STBC 2.
1 Radio-frequency; 2 Space Time Block Coding.
2.3. Channel Estimation Methods: (TDD or FDD?)
A non-stationary wireless channel needs to be re-estimated after every coherence time lap. Massive
MIMO systems were originally envisioned for time division duplex (TDD) operation, in which the
channel is periodically estimated in one direction and compensation can be applied in both directions
assuming reciprocity.
TDD systems have the following features:
1. The time required to acquire CSI does not depend on the number of BSs or users.
2. Only the BS needs to know the information about the channels to process antennas coherently.
In TDD systems, multi-user precoding in the downlink and detection in the uplink require CSI
knowledge at the BS. The resource, time or frequency needed for channel estimation is proportional to
the number of the transmit antennas.
In frequency division duplexing (FDD), uplink and downlink use different frequency bands
(different CSI in both links). The uplink channel estimation at the BS is done by letting all users send
different pilot sequences. To get the CSI for the downlink channel, the BS transmits pilot symbols to all
users. The users respond by the estimated CSI for the downlink channels [4].
CSI can be estimated at the receiver side only, or at both at the transmitter and the receiver.
Estimation at both sides has some advantages. The CSI does not have to be transmitted, which yields
low latency and high capacity. In addition, more power can be allocated to the (OFDM) subchannels
with higher channel gain. Schemes with estimation at the receiver side only experience higher outage
probability with fast fading channels but have lower complexity.
As the number of BS antennas goes up, the time required to transmit the downlink pilot symbols
increases. In addition, as the number of BS antennas grows, FDD channel estimation becomes almost
impossible and a TDD approach can resolve this issue. In TDD systems, due to channel reciprocity,
only CSI for the uplink needs to be estimated. In addition, linear MMSE based channel estimation can
provide near-optimal performance with low complexity [20].
Table 4 compares various channel estimation techniques of massive MIMO systems.
Table 4. Different channel estimation techniques of massive MIMO.
Ref. Channel Estimation Strategy System Type User Antennas Channel Type Performance Metric
[21], 2013
Compressive Sensing-Based Multiple Users Single TDD 1 , Flat-Fading Quasi-Static Estimation Error
[22], 2013
Direction of Arrival Estimation Multiple Users Single TDD, Ray Vectors Mean Square Errors and Capacity Loss
[23], 2014
Semi-Orthogonal Pilot-Assisted Multiple Users Single TDD, Rayleigh Overall Achievable Rates
[24], 2014
Closed-Loop Beam Alignment Single User Single FDD 2 , Gaussian Beamforming Gain
[25], 2014 Discriminatory Two-Users Multiple TDD, Rayleigh Flat Fading Power and MSE 3
[26], 2014
Low-Complexity Polynomial Single User Multiple TDD, Quasi-Static Flat-Fading
MSE
[27], 2014
Distributed Compressive CSIT 4 Multiple Users Multiple FDD, Quasi-static CSI 5 MSE
[28], 2014 Linear Estimation Multiple Users Single TDD, Narrowband Memoryless
Residue and Error Norms
[29], 2014
Improved Multicell MMSE 6 Multiple Users Single TDD, Rayleigh MSE
[30], 2014 CSIT Multiple Users Multiple FDD, Quasi-static CSI Mean Squared Error
[31], 2014
Spectrum-Efficiency Parametric Multiple Users Single FDD, Rayleigh Fading Mean Squared Error
[32], 2015 Blind Multiple Users Single TDD, NA MSE
[33], 2015
Gaussian-Mixture Bayesian Learning Multiple Users Single TDD, NA MSE and Average User Rate
[34], 2015 Subspace-Based Multiple Users Single TDD, Narrow band Flat Fading
Bit Error Rate and Eigen Value Clusters
[35], 2015
Simple DFT 7 -Aided Spatial Basis Expansion Multiple Users Single TDD, Flat Fading
The Average Achievable Sum Rate and MSE
[36], 2015 Bayes-Optimal Joint Multiple Users Single TDD, Flat Block Fading
Symbol Error Rate and MSE
[37], 2015 Adaptive Semi-Blind Multiple Users Single NA, TDD Capacity and MSE
[38], 2015 Imperfect Single User Single TDD, Spatially Correlated
BER 8
[39], 2015
Atomic Norm Denoising-Based Multiple Users Single TDD, Flat-Fading Quasi-Static Estimation Error
[40], 2016
Structured Compressive Sensing-Based Spatio-Temporal
Single User Single FDD, Fast time-varying
Mean Squared Error, BER, and Average Throughput
[41], 2016 Bayes Multiple Users Single TDD, Flat block fading MSE, and SER 9
[42], 2017
Eigenvalue Decomposition Multiple Users Single TDD, Fast fading Rate Loss, and SER
[43], 2017 Beam-Blocked Multiple Users Single FDD, Spatio Correlation Channel
MSE, Achievable Rate, and Reconstruction SNR 10
[44], 2017
Joint Angle-Delay Subspace Multiple Users Single TDD, Flat Rich Scattering
Projection Error Power, Path Number, and MSE
[45], 2017 Beam-Domain Multiple Users Multiple TDD, Block-fading Mean Squared Error, and BER
[46], 2017
Low Rank Covariance Matrix Multiple Users Single TDD, Flat Rayleigh fading Normalize MSE
1 Time Division Duplex; 2 Frequency Division Duplex; 3 Mean Squared Error; 4 Channel State Information at
the Transmitter; 5 Channel State Information; 6 Minimum Mean Squared Error; 7 Discrete Fourier Transform;
8 Bit Error Rate; 9 Symbol Error Rate; 10 Signal-to-Noise-Ratio.
Table 5. Cont.
Ref. Detection strategy System Type User Antennas Channel Type Performance Metric
[61], 2012
Interference Cancellation Single-user Multiple Complex Gaussian Achievable rate and Bit Error Rate
[62], 2012
Interference Cancellation Multiple Users Multiple Complex Gaussian Bit Error Rate
[63], 2012
Interference Cancellation
Single and Multiple Users Multiple Multipath Discrete-Time Block Fading Bit Error Rate
[64], 2012
Interference Cancellation Single User Multiple Block Fading Bit Error Rate
[65], 2014
Interference Cancellation Single User Multiple NA Bit Error Rate
[66], 2014
Interference Cancellation Multiple Users Multiple NA Bit Error Rate
[67], 2014
Interference Cancellation Multiple Users Multiple Complex Gaussian Bit Error Rate
[68], 2016
Interference Cancellation Multiple Users Single Flat Fading Bit Error Rate, and Average Number of Computations
[68], 2017
Interference Cancellation Multiple Users Single Flat Fading Bit Error Rate
[69], 2007 Linear Multiple Users Multiple Rayleigh Block Fading Bit Error Rate
[70], 2009 Linear Single User Multiple Rich-Scattering Flat-Fading Bit Error Rate
[71], 2011 Linear Multiple Users Multiple Frequency-Flat Fading
Empirical Cumulative Distribution and Bit Error Rate
[72], 2011 Linear Single User Multiple Block Fading Bit and Packet Error Rate
[73], 2012 Linear Single User Single Two-Way Relay Bit Error Rate
[74], 2013 Linear Multiple Users Multiple NA Block Error Rate
[75], 2013 Linear Single User Multiple Flat Fading Bit Error Rate
[76], 2013 Linear Single User Multiple Time-Varying Flat Fading Bit Error Rate
[77], 2013 Linear Single User Multiple NA Bit Error Rate
[78], 2016 Linear Multiple Users Single Block Flat Fading Sum Rate
[79], 2008 Local Search Multiple Users Single Rayleigh flat Bit Error Rate
[80], 2015 Local Search Single User Multiple NA Bit Error Rate
[81], 2016 Local Search Multiple Users Single Flat Fading
Bit Error Rate, and Average Number of Arithmetic Operations
[82], 2016 Local Search Multiple Users Single Quasi-Static Flat Fading
Bit Error Rate, and Normalized Spectral Efficiency
[83], 2007 (^1) LR-Aided Multiple Users Multiple NA Bit, Packet error rate and Throughput
[84], 2008 LR-Aided Multiple Users Multiple Flat-Fading Quasi-Static Bit Error Rate
[85], 2010 LR-Aided Multiple Users Multiple Rayleigh faded Bit Error Rate
[86], 2010 LR-Aided Single User Multiple Flat-Fading Bit Error Rate
[87], 2011 LR-Aided Single User Multiple Flat-Fading Bit Error Rate
[71], 2011 LR-Aided Single User Multiple Frequency-Flat Fading
Empirical Cumulative Distribution Function and Bit Error Rate
[88], 2012 LR-Aided Single User Multiple Quasi-Stationary (Block Fading)
Average Orthogonality Defect and Bit Error Rate
[89], 2012 LR-Aided Single User Multiple Rayleigh Flat-Fading Bit Error Rate
[90], 2012 LR-Aided Single User Multiple NA Bit Error Rate
[75], 2013 LR-Aided Single User Multiple Flat Fading Bit Error Rate
[91], 2014 LR-Aided Single User Multiple Flat Fading Bit Error Rate
[91], 2014 LR-Aided Three-User Multiple Frequency Flat Fading Bit Error Rate
[92], 2014 LR-Aided Single User Multiple Rayleigh Flat-Fading Channel Correlation Effect and Bit Error Rate
Table 5. Cont.
Ref. Detection Strategy System Type User Antennas Channel Type Performance Metric
[93], 2016 LR-Aided Multiple Users Multiple Rayleigh Flat-Fading Bit Error Rate, Sum Rate, and Plog Cond
[94], 2016 LR-Aided Multiple Users Multiple Quasi-Static Block Fading Bit Error Rate
[95], 2017 LR-Aided Multiple Users Single Rayleigh Flat-Fading Bit Error Rate, and Average Flops
[96], 2005 2 MCMC Single User Multiple Flat Fading Bit Error Rate
[97], 2007 MCMC Single User Multiple Flat Fading Bit Error Rate
[98], 2008 MCMC Single User Single Block Fading Bit Error Rate
[58], 2009 MCMC Single User Multiple NA Bit Error Rate
[99], 2011 MCMC Single User Multiple NA Bit Error Rate
[100], 2011 MCMC Single User Multiple NA Bit Error Rate
[101], 2012 MCMC Multiple Users Multiple Frequency Non-Selective Fading Bit Error Rate
[102], 2015 MCMC Multiple Users Single NA Bit Error Rate
[103], 2016 MCMC Multiple Users Single NA Bit Error Rate
[104], 2016 MCMC Multiple Users Single NA Bit Error Rate
[105], 2006 Optimum Detection Single User Multiple Uncorrelated Rayleigh Fading Bit Error Rate
[106], 2007 Optimum Detection Single User Multiple Quasi-Static Frame Error Rate
[107], 2007 Optimum Detection Single User Multiple Flat Rayleigh Fading Bit Error Rate
[108], 2009 Optimum Detection Multiple Users Multiple NA Bit Error Rate
[109], 2009 Optimum Detection Single User Multiple Block fading Frame Error Rate
[110], 2015 Optimum Detection Multiple Users Single Rayleigh Fading Bit Error Rate, and Flops
[111], 2016 Optimum Detection Multiple Users Single Rayleigh Fading
Bit Error Rate, Frame Error Rate, and Normalized Info Rates
[112], 2006
Probabilistic Data Association Multiple Users Multiple Quasi-Static Rayleigh Fading Bit Error Rate
[113], 2008 Probabilistic Data Association Single User Multiple NA Bit Error Rate
[114], 2009
Probabilistic Data Association Single User Multiple NA Bit Error Rate
[115], 2011
Probabilistic Data Association Single User Multiple NA Bit and Symbol Error Rate
[115], 2011
Probabilistic Data Association Single User Multiple NA Bit Error Rate
[116], 2013
Probabilistic Data Association Multiple Users Multiple Nakagami-m Fading Bit Error Rate
[117], 2013
Probabilistic Data Association Multiple Users Multiple Nakagami-m Fading Bit Error Rate
[118], 2013
Probabilistic Data Association Single User Multiple Nakagami-m Fading Bit Error Rate
[119], 2017
Probabilistic Data Association Multiple Users Single Flat Rayleigh Fading Bit Error Rate
[120], 2008 Soft-Input Soft-Output Multiple Users Single Flat Rayleigh Fading Bit Error Rate
[121], 2009 Soft-Input Soft-Output Multiple Users Single Rayleigh Multi-Path Fading
Average Complexity, and Rate
[122], 2014 Soft-Input Soft-Output Multiple Users Single Rayleigh Fading Frame Error Rate
1 Lattice Reduction; 2 Monte Carlo Markov Chain.
There are optimal detectors such as Maximum Likelihood Detectors. Local search detectors also
seek for optimal solution. However, these methods have an issue of huge problem size, as well as the
lack of knowledge of the problem structure. The good thing about local search is its neighborhood
function that guides the search to a right solution. Another popular technique is the polynomial time
approximation algorithm, but it gives an inferior solution.
a large number of antennas to increase the data rate without increasing the bandwidth [ 5 ]. PTP
systems usually assume frequency-flat and slow fading channels.
- MU-MIMO: Where the communication is between a BS and multiple user terminals.
Figure 4 shows a PTP MIMO system. The BS has M antennas, and it transmits data
(a vector-valued signal) to a user having K antennas. This transmitted vector is multiplied by
the channel matrix to produce the received signal vector. Different users are served over different
time/frequency blocks by time division/frequency division multiplexing.
An extensive discussion on PTP MIMO is presented in the following papers:
The authors in [ 136 ] studied Array Beamforming Synthesis and related areas. The existing
beamforming techniques for PTP MIMO lack providing efficient beamformers especially in certain
situations such as under different power constraints or array sizes, certain types of channels, and with
random initializations. To solve this problem, they proposed an iterative algorithm that specifies
transmit and receive beamformers based on various channel information available to the transmitter
and the receiver.
Figure 4. Point-to-point massive MIMO link.
In [ 137 ], the authors introduced an optimum linear precoder imposed on both sum-power
and maximum eigenvalue power. In [ 138 ], the authors discussed the most spectral-efficient power
allocation strategy and specified whether it is energy efficient or not. The proposed approach in [ 139 ]
optimally switches between beamforming and Orthogonal Space–Time Block Coding by varying the
periodicity of feedback intervals and varying the amounts of channel state information for mobile users
to determine the optimum diversity feedback. The approach in [ 140 ] proposed a new adaptive symbol
mapping scheme for PTP MIMO by disordering the transmitted symbols in a frame using dynamic
mapping (either by changing the allocation order of the symbols on the antennas or by applying a
scrambling process that reverses the symbols sign). The aim of doing this was to increase the symbols’
received power and to reduce the interference between the symbols.
Table 7 compares PTP and MU-MIMO, regarding implementation and precoding complexity,
error rate, rate gain and, operation flexibility [4].
PTP MIMO is not very suitable for massive MIMO due to the following reasons:
- Training time is related to the number of antennas and becomes too high as the number of
antennas grows.
- Independent electronics chains are required for each antenna; hence, as the number of antennas
increases, the system becomes very complicated and expensive.
- Multiplexing gains fall near the edge of the cell.
- Line-of-sight conditions for compact arrays permits only one data stream [1].
MU-MIMO alleviates some of the pernicious effects of PTP MIMO.
Beam Forming and Multiplexing with Millimeter Waves
Millimeter wave phased arrays have been devised and studied for diverse applications. Recent
works have given much concern to digital beamforming and spatial multiplexing using millimeter
wave frequencies [141].
There are many benefits of using massive mmWave multi-antenna systems, and these include the
following [8]:
- It has a significantly smaller form factor than designs established at current frequencies.
- Free space path loss (PL) would ultimately impose an upper limit on cell size. Path loss can
be beneficial in small-cell scenarios since it limits inter-cell interference and allows greater
frequency reuse.
- Growth in the number of antennas in the array, improves array gain, extends the communication
range and helps to beat PL.
- Allow dramatic increases in user bandwidth to hundreds of megahertz or even a few gigahertz
(and hence symbol periods on the order of 1 to 10 ns or less).
- Frequency selective fading may need to be addressed through either equalization or modulation.
Table 7. Difference Features Between Point-to-Point and MU-Massive MIMO.
Point-to-Point MIMO MU-MIMO
Easy to implement Not easy in capacity-achieving schemes
High sum-capacity of uplink Exactly the same
Less sum-capacity of downlink Higher sum-capacity of downlink
Users use single antenna terminals Users use single antenna terminals
More affected by the propagation environment Less affected by the propagation environment
User Selection is not flexible Flexible user choice and scheduling
Complex precoding Simple precoding
Optimal solutions to beamforming Downlink beamforming requires CSI 1 knowledge at the BS 2
Less rate gain High rate gain
More error rate Less error rate
Knowledge of uplink CSI Full knowledge of uplink and downlink CSI.
Less complexity of coding/decoding The growing complexity of coding/decoding.
Less time to acquire CSI Significant time is spent acquiring CSI, which grows with both the number of BSs and users
1 Channel State Information; 2 Base Station.
An increasing number of papers in the literature discuss mmWave massive MIMO for next
generation 5G wireless systems. In [ 141 ], the authors gave an introduction of mmWave massive MIMO,
and then highlighted the importance of digital beamforming and spatial multiplexing as a future trend
replacing the old analog mmWave phased arrays. In addition, they briefly spoke about the design
considerations, the problems facing proper transmission like interference management, and loss of
channel orthogonality. In the end, they explained the antenna and radio frequency (RF) transceiver
architecture.
Table 8 compares the different beamforming techniques of mmWave massive MIMO.
2.6. Precoding Techniques (Linear or Nonlinear?)
It is well known that MIMO effectively utilizes multiple channels between the BS and users by
using appropriate (space-time) coding to increase system throughput.
On the other hand, the massive MIMO system works by space division multiplexing by knowing
the CSI of every link connecting the BS to a user.
Table 9. Cont.
Ref. Technique Users User Antennas Channel Type Performance Metric Results
[160],
Discrete-Phase Constant Envelope
Multiple Users Single Rayleigh Fading
Avereage Interference Power, Rate Loss, and Rate Per User
Degaraded Compared to the Continuous Phase Algorithm, and Moderate Compared to the Conventional Ones
[161], 2017 Cell-Edge-Aware Multiple Users Single Quasi-Static Coverage Probability, and Sum Rate Per Cell Extensive
[162],
Orthogonal Random Multiple Users Multiple Block Constant Fading Coverage Probability Extensive
1 Minimum Mean Squared Error; 2 Additive White Gaussian Noise; 3 Signal-to-Noise-Ratio; 4 Zero Forcing;
5 Maximum Ratio Transmission.
Received signals from different terminals are combined in the uplink using appropriate decoding.
The more the antennas are used, the finer the spatial focusing can be so that a large array is built in
practice. The use of nonlinear but power efficient RF front-end amplifiers are preferred to minimize
power consumption in this high bit rate scenario (Note that energy per bit will decrease in proportion
to the square bit rate. Hence, the transmit power has to be very high at Gigabit data rates.) Therefore,
to avoid signal distortion at nonlinear amplifiers, often the transmit signal is required to have
a low peak-to-average-power-ratio (PAPR), which is difficult to achieve, especially in orthogonal
frequency-division multiplexing (OFDM) environments. Several PAPR reduction techniques and
precoding can hence be fruitful. Furthermore, precoding with such power-efficient amplifier constraints
leads to improvement in the power efficiency of the entire system.
Low-complexity precoding methods are mandatory and critical to minimize the computational
complexity of the precoder [ 19 ]. A recent study mentions that single-carrier modulation (SCM)
can, in theory, fulfill near-optimal sum rate performance in massive MIMO systems operating at
low-transmit-power-to-receiver-noise-power ratios, distinct from the channel power delay profile and
with an equalization-free receiver [ 141 ]. In SCM, the PAPR performance is also optimally maintaining
a constant envelope.
For conventional MIMO systems, both nonlinear precoding and linear precoding techniques
are used without preferences, although nonlinear methods, such as dirty-paper-coding (DPC)
and lattice-aided methods, have better performance with higher implementation complexity. Unlike the
conventional MIMO, massive MIMO systems use linear precoders, such as maximal ratio combining
(MRC), matched filtering, conjugate beamforming, minimum mean squared error (MMSE) and
zero-forcing (ZF) [4].
Table 10 makes a comparison between MRC, MMSE, and ZF precoding techniques.
In addition, Figure 5 shows a comparison between MMSE, ZF, and MRC precoding techniques vs.
the number of BS antennas.
In MRC, the multiple antenna transmitter uses the channel estimate of a terminal to maximize
the strength of that terminal’s signal by adding the signal components coherently. MRC precoding
maximizes the SNR and works well in the massive MIMO system, since the base station radiates low
signal power to the users on average.
Table 10. Comparison between the performance of ZF precoding, MMSE precoding, and
MRC precoding.
Performance Metric ZF^1 Precoding MMSE^2 Precoding MRC^3 Precoding
Achievable rate Optimum (very high) Medium Less
Performance with respect to power
Better at high transmission power
Best performance at high and low transmission powers
Better at low transmission power
Performance at high SNR 4 Better Converges to ZF Less
Performance at low SNR Less Good Good
BER 5 High Low Highest
Number of served users Low Highest High
Interferences ( Inter-cell and Multiuser) Suppresses Treated as extra additive noise More
Capacity Low Linear capacity growth with antennas Very low
Number of antennas Needs more antennas Capability to work with fewer antennas More is better
Channel matrix
Uses Pseudo-inverse of the estimated channel matrix to cancel Inter user interference
Uses MSE of estimated channel matrix
Uses the complex conjugate of the estimated channel matrix
Working condition
Not necessarily able to work under high inter-cell interference
Capability to work under high inter-cell interference conditions
Cannot work under very high inter-cell interference
1 Zero Forcing; 2 Minimum Mean Squared Error; 3 Maximum Ratio Combining; 4 Signal-to-Noise-Ratio;
5 Bit Error Rate.
Number of BS Antennas 104
Spectral Efficiency [bits/s/Hz/cell]
Comparison between the Spectral Efficiency of Various Precoding Methods
MMSE ZF MRC
Figure 5. An illustration of the spectral efficiency of a massive MIMO system serving 16 users in under
the Rayleigh fading channel (with various precoding methods).
ZF precoding is a method of spatial signal processing by which the transmitter can null out
multiuser interference signals. In general, ZF precoder performs well under high SNR conditions.
The ZF precoder outperforms MRC, as shown in Figure 5 in performance as well as in
computational complexity. It also suppresses inter-cell interference at the cost of reducing the array
gain [ 6 ]. It is noted that spectral efficiency increases as the number of BS antennas grows. In addition,
the figure shows the superiority of the performance of MMSE, especially in massive MIMO.
MMSE precoding is the optimal linear precoding in a massive MIMO downlink system.
This technique uses the mean square error (MSE). The Lagrangian technique is used to optimize
this precoder, using the average power of each transmitting antenna as the constraint.
Distance (m) 104
Distance (m)
104 Two-tiers Cellular Network
Macro Cells Pico Cells
Figure 6. An illustration of a Poisson point process (PPP)-based two-tier cellular network deployment.
A 20 km × 20 km area, consisting of femto-cells (crosses) and macrocells (dots), is shown.
Table 11. Comparison between homogeneous and heterogeneous MIMO systems.
Heterogeneous MIMO Homogeneous MIMO
Models the actual systems, which are composed of multiple networks operating together at the same time, and area
Non-realistic
High sum-capacity in the order of thousands Capacity increase, but not as HetNets
Users can access any BS 1 in any tier Users access only the closest BS
More interference is considered (inter-tier interference) Less affected by interference
Flexible user choice and scheduling User Selection is not flexible
More flexibility and degrees of freedom Less interference
Optimal solutions to beamforming Downlink beamforming requires CSI 2 knowledge at the BS
Networks with different capabilities Limited
More error rate Less error rate
BSs have different transmit powers, and multi-access methods Everything is fixed
Less overhead load Users are overloaded with the long range transmission to BS
Network life-time is more Less network life-time
1 Base Station; 2 Channel State Information.
Authors of [ 167 ] studied multi antenna HetNets with zero-forcing precoding. They compared the
coverage probability and rate per user for both open access (where users are allowed to access any BS
in any tier) and closed access networks (where users are granted access to certain BSs in restricted tiers).
The authors used a cell association criterion based on the maximum Signal to Interference Plus Noise
Ratio (SINR). In addition, the authors compared the performance with various combinations of
multiple antenna techniques. The performance when the BS is serving a single user in each resource
block (by SISO or single user beamforming (SU-BF) is compared with MIMO configuration serving
multiple blocks (by space division multiple access (SDMA)). However, the approximations need
more characterizations. In addition, the numerical integrals need extra computational tools to obtain
the results.
In [ 168 ], the authors introduced the fractional frequency reuse (FFR) technique to manage the
cross-tier interference (strict FFR and soft frequency reuse). In addition, the authors derived the
coverage probability for open-access and closed-access networks (different association policies) and the
average rate for the cell edge users. Finally, the authors compared the performance of different FFR
and access cases under the full SDMA and SU-BF.
In [ 169 ], the energy efficiency of different MIMO diversity schemes and antenna configurations
using adaptive modulation of a two-tier network is studied to ensure a minimum quality of service
(QoS). Energy is saved while obtaining the same throughput by using femto-cells with sleeping
mode capabilities, where only a few of the available antennas are used. This paper identifies that
the diversity schemes that provide the highest throughput is different than the ones that achieve the
highest energy efficiency.
Finally, in [ 170 ], the authors derived general and asymptotic success probability expressions for
multi-user HetNets with ZF precoding, using a novel Toeplitz matrix representation. In addition,
they showed the effect of the BS density on the success probability and derived an optimal BS density
for obtaining the maximum area spectral efficiency (ASE) while guaranteeing a certain link reliability.
This paper is straightforward with a simple system model. More sophisticated system models should
be investigated.
In addition, the advantages of introducing mmWave frequency operation in HetNets is discussed
in [ 171 ]. The authors discussed the potentials and challenges of the 5G HetNet wireless networks,
which merge mmWave technologies into a massive MIMO approach. First, they discussed the extended
requirements for 5G wireless networks with an enormous number of devices that demand more
concealment, data rate, better energy and cost efficiency. Then, they discussed the difficulties including
traffic arrangement, radio resource management, mobility management, and low-cost beamforming.
In the end, they presented some design and case studies to illustrate how to address some of the
challenges in 5G MIMO HetNet.
4. Conclusions
Massive MIMO is an innovative technology that helps in the achievement of higher system
throughput and reliable transmission for 5G and beyond wireless networks.
In this paper, we discussed major elements of massive MIMO networks, namely pilot usage,
precoding, encoding, detection, and beamforming. We provided a detailed overview of some of
the research efforts done in this area so far. We observe that fast booming HetNets would be more
promising to improve data rates and provide flexibility in user-BS association.
There are many interconnected design issues that need to be properly understood and solved
before widespread deployment of the massive MIMO technology. Several open research challenges
are still facing the progress and development of this emerging technology.
More research is needed to introduce new adaptive beamforming techniques to achieve higher
received symbol power and less interference. In addition, introducing efficient beamformers for PTP
networks to work under different constraints and with different types of channels would be beneficial
for enabling PTP widespread application in massive MIMO systems.
As detection becomes harder when the number of BS antennas increases, more advanced
signal processing methods are required for better detection and are associated with introducing
low complexity optimum and nonlinear detectors, and precoders to improve the performance and
reduce the computational complexity.
Introducing new techniques to reduce the training time, especially when the number of antennas
increases is needed, will, in turn, improve the performance of FDD systems in massive MIMO to
improve channel gain, capacity, received power, and reduce latency.
As the number of interfering cells increases, pilot contamination exponentially grows up,
and prevents proper system function. Introduced methods to reduce pilot contamination are very
limited and aim to reduce the effect of the problem, but do not provide a final solution.
The benefits and issues of using the mmWave frequency band, and its application on beamforming,
channel estimation, and precoding techniques in homogeneous and heterogeneous systems, need
