# Directional Modulation: A Secure Solution to 5G and Beyond Mobile Networks

Feng Shu, Yaolu Qin, Rqing Chen, Ling Xu, Tong Shen, Siming Wan
Shi Jin, Jiangzhou Wang, and Xiaohu You This work was supported in part by the
National Natural Science Foundation of China (Nos. 61771244, 61501238,
61702258, 61472190, and 61271230), in part by the Open Research Fund of
National Key Laboratory of Electromagnetic Environment, China Research
Institute of Radiowave Propagation (No. 201500013), in part by the Jiangsu
Provincial Science Foundation under Project BK20150786, in part by the
Specially Appointed Professor Program in Jiangsu Province, 2015, in part by
the Fundamental Research Funds for the Central Universities under Grant
30916011205, and in part by the open research fund of National Mobile
Communications Research Laboratory, Southeast University, China (Nos. 2017D04
and 2013D02).

###### Abstract

Directional modulation (DM), as an efficient secure transmission way, offers
security through its directive property and is suitable for line-of-
propagation (LoP) channels such as millimeter wave (mmWave) massive multiple-
input multiple-output (MIMO), satellite communication, unmanned aerial vehicle
(UAV), and smart transportation. If the direction angle of the desired
received is known, the desired channel gain vector is obtainable. Thus, in
advance, the DM transmitter knows the values of directional angles of desired
user and eavesdropper, or their direction of arrival (DOAs) because the
beamforming vector of confidential messages and artificial noise (AN)
projection matrix is mainly determined by directional angles of desired user
and eavesdropper. For a DM transceiver, working as a receiver, the first step
is to measure the DOAs of desired user and eavesdropper. Then, in the second
step, using the measured DOAs, the beamforming vector of confidential messages
and AN projection matrix is designed. In this paper, we describe the DOA
measurement methods, power allocation, and beamforming in DM networks. A
machine learning-based DOA measurement method is proposed to make a
substantial SR performance gain compared to single-snapshot measurement
without machine learning for a given null-space projection beamforming scheme.
However, for a conventional DM network, there still exists a serious secure
issue: the eavesdropper moves inside the main beam of the desired user and may
intercept the confidential messages intended to the desired users because the
beamforming vector of confidential messages and AN projection matrix are only
angle-dependence. To address this problem, we present a new concept of secure
and precise transmission, where the transmit waveform has two-dimensional even
three-dimensional dependence by using DM, random frequency selection, and
phase alignment at DM transmitter.

##  I Directional modulation: concept and system

Due to the broadcast nature of wireless transmission, confidential information
is easily intercepted by malicious users, which will expose wireless networks
to serious secure risk. Therefore, secure transmission, storage, processing,
and protection of confidential information become extremely important research
topics in wireless networks in recent years. Additionally, there is an
increasing demand to design secure transmission methods to protect the
legitimate users from being overheard. Recently, as millimeter wave (mmWave)
massive multiple-input multiple-output (MIMO), unmanned aerial vehicle (UAV),
and internet of things (IoT) emerge, how to securely transmit confidential
messages in line-of-propagation (LoP) channel is becoming a hot research area.
Directional modulation (DM), as an inherent secure method in LoP channel,
attract more and more research activities from both academia and industry
communities.

Figure 1: Schematic diagram of directional modulation network. Figure 2:
Schematic diagram of smart directional modulation transceiver, where CM stands
for confidential messages.

In Fig. 1, a concept diagram is presented to show the basic idea of DM. In
this figure, there are one DM transmitter with multiple transmit antennas, two
eavesdroppers, and one desired user. The DM transmitter sends its confidential
messages to the desired user such that the two eavesdroppers cannot intercept
the confidential messages. By exploiting the directive property generated by
antenna-array-based beamforming with the help of artificial noise (AN)
projection, the DM transmitter transmits the confidential message to the
desired direction and interferes with the eavesdroppers by AN projection. Due
to the joint operation of AN projection and beamforming, the confidential
messages can be securely and successfully transmitted to the desired user, and
AN severely corrupts the eavesdroppers. We propose a smart DM transceiver
shown in Fig. 2. Here, one of machine learning methods, Bayesian learning in
[1] is adopted to improve the measurement precision of DOA angles, which
subsequently serves for designing the precoding vector and AN projection
matrix at DM. Due to channel noise and interference in channel, there exists
the DOA measurement errors. As shown in [2], a high-precision DOA estimation
means a large secrecy rate provided that a fixed beamforming scheme is given.
In what follows, the number of antennas at DM transmitter is assumed to be
$N$.

##  II DOA measurement, and Machine learning

For secure DM, high-resolution DOA measurement and high-precise DOA error
density estimation are significantly important for DM transmitter. As stated
in [2], [3], perfect DOA measurement results in performance improvement since
expected information and AN can be accurately transmitted to the desired
direction and eavesdropping direction, respectively. Due to ultra-high-
resolution of spatial direction, and super-high-spectral efficiency, massive
MIMO has drawn tremendous research attention from academia and industry
communities [4]. If massive MIMO behaves as a receive array, DOA estimation
precision will be dramatically improved due to its ultra-high-resolution of
spatial direction.

The estimated signals can be classified into two categories: narrowband
signals and wideband signals [5]. The narrowband signals are transmitted with
the same frequency. However, in wideband signal DOA estimation problems,
several frequency bins carry different information corresponding to source DOA
angles. This generates diversity and processing gain for DOA estimation. The
main problem in wideband DOA estimation is how the information at each
frequency can be combined to obtain the most accurate DOA information. Two
main types of wideband processing are coherent and noncoherent. In coherent
wideband processing, the covariance matrix at each frequency is combined
coherently using a transformation and the final covariance matrix is used for
DOA estimation. In noncoherent wideband processing, the DOA at each frequency
is estimated separately and the results are combined noncoherently.

Many typical DOA estimation algorithms have been proposed and analyzed. Capon
algorithm is maximum likelihood estimation of power which aims at maximizing
the signal-to-interference ratio (SINR). Schmidt developed a more popular
method, i.e., the multiple signal classification (MUSIC) [6] algorithm, which
is a high-resolution eigen-structure-based DOA-finding method.

Considering the need of high-resolution DOA measurement in physical layer
secure communication and the advantages of massive MIMO systems [4], adopting
massive MIMO in DOA measurement is reasonable. However, as the number of
antennas tends to be large-scale, the computational amount, circuit complexity
and cost of digital implementation become too high for commercial
applications. Therefore, a hybrid analog and digital (HAD) structure is a
natural choice, which will strike a good balance among computational amount,
circuit cost, and circuit implementation complexity. In [7], the authors
presented the low-complexity DOA estimation algorithm based on Root-MUSIC
method and hybrid structure which can reduce both the computational complexity
and hardware cost.

In a DM network, the beamforming vector and AN projection matrix depend
heavily on the precision of DOA measurement. How to achieve a high-precision
DOA measurement, machine learning is a new and advanced method to address such
a problem. In this article, we present a Bayesian learning (BL) based method
to improve the DOA measurement precision at DM transmitter with fully-digital
(FD) structure. It is particularly noted that the idea can be readily extended
to the HAD structure. Firstly, the DM transmitter with FD structure acts as a
receiver, and takes a number of snapshots. By using the proposed method Root-
MUSIC, we can obtain a training data set (TDS) of measured DOA values by
taking multiple snapshots and its size is denoted as $K$, where the number of
sampling points is $M$. As shown in Fig. 3, the histogram method in machine
learning is adopted to do density estimation of DOA measurement errors. In
accordance with this figure, it is clear that the DOA measurement errors
approximately obeys the Gaussian distribution. Subsequently, the DOA
measurement error is viewed as a Gaussian distribution in the following. The
BL is introduced to estimate the mean and variance of the desired DOA
measurement error, where the prior distributions of angle mean and variance
are assumed to be uniformly distributed.

Fig. 4 illustrates the curves of root mean squared error (RMSE) of DOA
measurement versus signal-to-noise ratio (SNR) for BL with different sizes of
training data set, where the size of TDS is $K$. It is very clear that as the
size $K$ of TDS increases from 1 to 20, the DOA measurement precision is
improved gradually and obviously.

Fig. 5 demonstrates the curves of secrecy rate (SR) versus signal-to-noise
ratio (SNR) for in a DM network as shown in Fig. 1 , where null-space
projection (NSP) method is adopted to design AN projection matrix and matched
filter (MF) is for the precoding vector of confidential message, the DOA
values measured by BL is directly substituted into the expressions of NSP
injection and MF beamforming. As shown in Fig. 5, it is seen that the
achievable SR performance gain achieved by increasing the size $K$ of TDS is
appreciated, especially in the low SNR region. However, as SNR increases, the
gain will decrease slowly and gradually. It is particularly noted that the DOA
measurement for desired user and eavesdropper is done by receiving the
transmit signal from desired user and eavesdropper in the first time slot once
the DM transceiver behaves as a receiver. In the second time slot, via the
beamforming scheme, the DM transceiver operates in transmit model, sends the
confidential messages to the desired user, and projects AN towards the
eavesdropper.

Figure 3: Histogram of DOA measurement errors.
Figure 4: Root mean squared error of BL-based DOA measurement versus
SNR($M=4$).
Figure 5: Secrecy rate versus SNR with different sizes of training data
set($M=4$).

##  III Power allocation, robust beamforming, and AN projection for DM

As an extremely important secure physical layer wireless transmission way, DM
can enable confidential messages transmit along a specified direction. In
particular, DM is a transmitter side technology that projects digitally
modulated signals into a pre-specified safe direction and simultaneously
distorts the constellation formats of the signals in other directions by AN
projection. The traditional DM technology is mainly investigated in the radio
frequency front end. One kind of DM transmitters that rely on near-field
coupling effects, and this kind of DM transmitters can be regarded as passive
DM transmitters because all parasitic elements are passively excited. In this
case, the combinations of each switch state on near-field passive reflectors
can form a unique far-field radiation pattern that can be converted into
detected constellation points in IQ space along each spatial direction in free
space. After the tremendous measurements of multiple modes for a large number
of possible switch states combinations, the available constellation patterns
in the desired direction can be selected and the corresponding switch settings
for secure transmission of each symbol can be obtained. However,
constellations along other unselected directions are distorted in a complex
and almost unpredictable way due to the complicated passive near-field
diffraction effect along spatial direction. Besides, the complex interaction
in the near field and their spatially correlated transformation with the far
field make the synthesis of passive DM transmitters immensely difficult.

Daly first proposed a method to simplify DM synthesis in [8], in which the
structures of the DM transmitters consist of actively driven antenna arrays
and is equipped with a reconfigurable phase shifter or radiator. Since each
array element is actively excited, this kind of DM transmitters is called
active DM array. In active DM arrays, the carrier signal needs to be modulated
by the baseband information data which controls the attenuator and the phase
shifter before being transmitted through the antenna array. In general, this
type of DM transmitter is synthesized by minimizing the value of an
appropriate cost function that sets the architecture parameters and predicts
system performance through iterative optimization. Based on the same physical
structure, some parameters such as quantization phase shifter, array element
spacing, and active element mode are studied exhaustively, respectively.

Another way to implement DM is performed via baseband signals. It is notable
that the author in [9] proposed a new theory that describes direction
modulation system with the expression of vector, and with the help of this
theory, the transmission characteristics of DM was achieved. This synthesis
method is also known as the orthogonal vector method. Compared with the
traditional synthesis method that implemented DM at RF front-end, this
synthesis method can be easily implemented in baseband signal by utilizing the
beamforming scheme and added AN, and in this case, it can further ensure that
different constellation points are transmitted in different time slots, in
other words, the dynamic DM. However, all these works are based on the perfect
situation of the desired direction angle, and they do not take the estimation
error of desired direction angle in actual scenarios into consideration.

(a) $\beta=0.2$ (b) $\beta=0.5$ (c) $\beta=0.8$

Figure 6: Histogram of Secrecy rate versus number of antennas at DM
transmitter.

In the recent several years, the DOA measurement error is exploited and some
robust beamforming methods of designing the beamforming vector of confidential
messages and projection matrix of AN were proposed [2, 10, 11]. The authors of
[2] derived a closed-form expression for the null space of the steering vector
along the desired direction, and a robust DM synthesis method based on
conditional minimum mean square error (MMSE) criterion was proposed to
minimize the distortion of constellation points along the legitimated users.
Subsequently, in [10], the authors extended the idea of [2] to multi-beam DM
scenarios in broadcasting systems, where a conditional maximizing signal-to-
leakage noise ratio (Max-SLNR) was presented to design the beamforming vector
of confidential messages and maximizing the signal-to-artificial-noise ratio
(Max-SANR) at the desired receivers was employed to design projection matrix
of AN. However, the two robust schemes[2, 10] need to know the PDF of DOA
measurement error in advance. This imposes a great burden on DOA measurement
operation. To address this problem , without the knowledge of distribution of
direction measurement error, a blind robust scheme of combining main-lobe-
integration and leakage were formed to design the beamforming vector of
confidential messages and AN projection matrix in multi-user multiple input
multiple output (MIMO) scenario. Additionally, the authors extend the
application of DM to a multi-cast scenario in [3]. In the extended work, two
novel schemes, maximum group receive power plus null-space projection scheme
and Max-SLNR plus maximum-AN-leakage-and-noise ratio scheme, were proposed to
improve the secrecy sum-rate.

How does the power allocation strategy between AN and confidential messages
affect? In [12], given a fixed beamforming scheme, an optimal power allocation
(OPA) strategy of maximizing secrecy rate for secure directional modulation is
presented and its closed-form formula is also derived. In Fig. 6, the SR
performance gain percentage achieved by OPA over three fixed typical power
allocation methods are demonstrated, respectively. Here, $\beta$ stands for
the PA factor for confidential messages. Observing the three figures, it is
very obvious that a small value $\beta$ means a small performance improvement.
In small-scale antenna array and low SNR region, the achievable SR performance
attained by OPA is relatively attractive. For example, at $N=8$, $\beta=0.2$,
and SNR=5dB, the SR performance gain percent is about $66\%$. This improvement
is very impressive.

##  IV Secure Precise Wireless Transmission

For a conventional DM network, if an eavesdropper moves inside the mainbeam of
the desired user and even has different distance to the DM transmitter
compared to the desired user, then it is still intercept the confidential
messages for the desired user. This leads to a serious secure issue. To
address the serious security problem faced by traditional DM, a new concept,
called secure and precise wireless transmission, was first proposed by the
authors in [13] and [14], where three key techniques, DM, random frequency
diversity, and phase alignment, are utilized to reach the secure and precise
transmission, which generates two-dimensional angle and distance dependence.
Now, there is another way to achieve secure and precise wireless transmission:
multi-relay cooperation with the aid of DM[15]. In other words, given angle
and range, the confidential message power can be transmitted and collected
inside a small neighborhood around the desired position, outside which there
exists very weak receive power seriously corrupted by AN and the confident
messages can not be detected successfully.

In [13], a random frequency diversity array was proposed which randomly shifts
the carrier frequencies in each different transmit antennas, and the frequency
shifting on each element has an independent and identically distributed
statistical property, decoupling the correlation between the distance and the
direction angle while guaranteeing the array’s dependence to the distance and
direction angle. In addition, the transmitter added AN to interfere with other
location of the eavesdropper, so that this scheme can significantly improve
the ergodic safety capacity of information transmission, and improve the
safety transmission performance.

Another secure precise transmission scheme with multi-relay-aided directional
modulation was also proposed in [15]. In this scheme, confidential messages
are transmitted by multiple relays, and utilize direction modulation on every
relay. All relays adjusted their directive main beams to the desired position
such that the power peak is formed by coherent superposition. Deviation from
this position, the receive confidential power add together not constructively
perhaps destructively. Furthermore, the combined signal is also seriously
corrupted by AN.

Due to the use of MIMO array and random frequency selection at transmitter,
where $N$ denotes the number of transmit antennas at DM transceiver, the
desired receiver requires $N$ RF chains to coherently combine all signals from
$N$ frequency bands. As $N$ tends to large scale, the circuit cost and
computational complexity at desired receiver will increase linearly and
dramatically. To reduce this cost, in [14], a secure and precise wireless
transmission with random subcarrier selection (RSS) based on OFDM and
direction modulation was proposed. This scheme reduces $N$ RF chains to only
one. At receiver, via the FFT/IFFT operation at basedband, in the frequency
domain the phase alignment is realized readily. Although the OFDM-based RSS
may dramatically reduce the circuit cost and computational complexity of the
receiver, the DM transmitter still keeps a high circuit cost. A HAD structure
at DM transmitter is a natural alternative.

(a) SINR versus elevation angle and distance (b) SINR versus azimuth angle and
distance (c) SINR versus azimuth and elevation angles

Figure 7: Average SINR over: (a) elevation angle and distance, (b) azimuth
angle and distance, and (c) azimuth and elevation angles, where $B=5$MHz.

In the above secure and precise wireless system [13, 14, 15], only two-
dimensional (2D) azimuth angle and distance were exploited. In reality,
transmitter and receiver can not be guaranteed to be in the same plane. How to
achieve precise wireless transmission in three-dimensional (3D) scene?
However, a practical environment is 3D: elevation angle, azimuth angle and
distance. It is also an interesting work to extend traditional 2D DM to 3D DM.
For a 3D DM, the beamforming scheme, including AN projection matrix and
confidential beamforming vectors in [14], is extended to the 3D polar
coordinate system. Fig. 7 shows the average SINR over any two coordinates with
the third coordinate being fixed, where the desired and eavesdropper
directions are 45∘, and 120∘. It is seen that only single SINR peak appears in
all three subfigures (a), (b), and (c). Outside the single peak, there are
only weak confidential message power seriously corrupted by AN. This confirms
the fact that the secure and precise transmission actually addresses the
secure problem of DM, where the traditional DM as shown in [13] has the
confidential message power mountain stretching from the DM transmitter to
infinity easily intercepted by those eavesdroppers who move inside the main
beam of the desired user.

Due to the above advantages of DM and its related improved version such as
secure and precise transmission, DM may extend its application fields to more
aspects. However, there still exist so many open problems to address in secure
and precise transmission, and DM fields. Here, we list multiple important ones
of them as follows:

  1. 1.

All above schemes only consider single desired user, How to extend the above
secure and precise wireless transmission to multi-user, broadcasting, and
multi-cast scenarios. In such a situation, the DM transmitter need to generate
multiple peaks of confidential message. This will place a great challenge on
how to design a set of random subcarriers, who forms multiple power peaks
corresponding to multiple desired receivers

  2. 2.

As the number of transmit antennas at DM transmitter tends to large-scale, the
circuit cost and complexity becomes a significant obstacle for practical
applications of DM. A FD structure is clearly infeasible. A HAD beamforming
structure is a natural choice. Sub-array structure in HAD can result in a
dramatic reduction in circuit cost and complexity. However, in such a
structure, there are open problems of how to offer high-precision DOA
measurement and robust beamforming scheme for DM.

  3. 3.

In wireless mobile communication, the relative motion among Alice, Bob, and
Eve will produce the Doppler shift. How to measure the DOA under Doppler shift
is a challenging task. Even how to jointly estimate Doppler shift and DOA is
also a new problem.

  4. 4.

DM is originally suitable for LoP channels. In multipath channel, multipath
effect will gather AN towards the desired receiver if the blocking object
locates at the eavesdropper direction. This effect is called the effect of
gathering AN due to multipath transmission. It will severely degrade the
performance of the desired receiver. How to combat this effect is also a major
challenge for DM. If this problem is solved, DM can extend its applications to
multipath channel, and even significantly enlarge its application fields.

##  V Conclusion

In this article, the great potential of directional modulation has been
highlighted as a key enabling secure technology for future fifth generation
(5G) cellular systems, IoT, UAV, smart transportation, and satellite
communications. We review its beamforming schemes, DOA estimation, power
allocation, and its improved version secure and precise transmission. The
technology achieves excellent security in LoP channels. There are still
several challenging problems ahead to exploit the full potential of the
technology. Also, we have raised several new open important research problems.
Finally, in our view, DM will achieve wide diverse promising applications in
the near future.

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FENG SHU is a professor with the School of Electronic and Optical Engineering
at Nanjing University of Science and Technology, Nanjing, China, also with
School of Computer and information at Fujian Agriculture and Forestry
University and awarded with Mingjian Scholar Chair Professor in Fujian
Province, China. He has published more 200 journal and conference papers on
signal processing and communications. His research interests include
statistical signal processing and low-complexity algorithms with applications
in wireless communications.
---

YAOLU QIN is a postgraduate student in the School of Electronic and Optical
Engineering at Nanjing University of Science and Technology, Nanjing, China.
Her research interests include massive MIMO, wireless localization, and DOA
measurement in wireless communications.
---

RIQING CHEN is a professor with School of Computer and information at Fujian
Agriculture and Forestry University, Fujian Province, China. He has published
more 50 journal and conference papers on signal processing and communications.
His research interests include statistical signal processing and low-
complexity algorithms with applications in wireless communications.
---

TONG SHEN is a PhD student in the School of Electronic and Optical Engineering
at Nanjing University of Science and Technology, Nanjing, China. His research
interests include massive MIMO, directional modulation, and DOA measurement in
wireless communications.
---

LING XU is a postgraduate student in the School of Electronic and Optical
Engineering at Nanjing University of Science and Technology, Nanjing, China.
Her research interests include massive MIMO, wireless localization, and DOA
measurement in wireless communications.
---

SIMING WAN is a postgraduate student in the School of Electronic and Optical
Engineering at Nanjing University of Science and Technology, Nanjing, China.
Her research interests include massive MIMO, wireless localization, and DOA
measurement in wireless communications.
---

SHI JIN is a professor School of Information Science and Enginering at
Southeast University, Nanjing, China. He has published more 100 journal and
conference papers on signal processing and communications. His research
interests include statistical signal processing and low-complexity algorithms
with applications in wireless communications.
---

JIANGZHOU WANG is currently the Head of the School of Engineering and Digital
Arts and a Professor of Telecommunications with the University of Kent,
Canterbury, U.K. He has authored over 200 papers in international journals and
conferences in the areas of wireless mobile communications and three books.
His research interests include statistical signal processing and low-
complexity algorithms with applications in wireless communications.
---

XIAOHU YOU is with Southeast University, first as an Associate Professor and
later as a Professor. He is also the Chief of the Technical Group of China
3G/B3G Mobile Communication R&D Project. His research interests include mobile
communications, adaptive signal processing, and artificial neural networks
with applications to communications and biomedical engineering.
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