Improved Hybrid Precoder Design for Secure mmWave MIMO Communications

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I. INTRODUCTION
The millimeter-waves (mmWaves) aim to provide a wide bandwidth around 200 times more than the present mobile communication systems by utilizing the upper part of the electromagnetic spectrum. These waveforms are realized to accommodate the challenging demands of upcoming fifthgeneration (5G) mobile communication systems such as higher data rate, diverse device connectivity, low latency, higher system capacity, and low energy consumption [1]. Still, it is very difficult to develop communication systems using mmWave bands owing to unavoidable degradation problems (e.g., penetration loss, propagation loss, and rain fading) [2]. However, shorter wavelengths of mmWaves support the deployment of large-scale antenna array structure to attain promising beamforming gainsthat allows more efficient utilization of spectrum. Since it is inappropriate to integrate radio frequency (RF) chain for Manuscript received 18 November, 2019; accepted 10 April, 2020. each antenna in mmWave communication systems causing cost and energy consumptionissues, it is practicle to exploit digital and analog hybrid multiple-input multiple-output (MIMO) system with an optimal number of RF chains [3], [4]. In addition, definite number of useful propagation paths are achievable by mmWave channels. To cope with this issue, narrow directional beam is achieved from hybrid precoder by utilizing extensive antenna array structure [5]. Despite the promising features offered by hybrid precoder, efficiency of mmWave communication systems is compromised due to analog precoding, which has certain magnitude and phase limitations. It is logical to utilize the low-resolution phase shifters (PSs) to avoid circuit and energy consumptioncomplications.
Security is also an inevitable issue in addition to the aforementioned in mmWave communication systems. The physical layer security (PLS) is realized as promising solution to guarantee secure transmission for the present and next-generation wireless systems [6]. It is obligatory to prevent information from undesired user (eavesdropper, Eve) since wireless communication systems are vulnerable to all the mobile users located in its vicinity due to the broadcast nature of their wireless links. The multi-antennas in mmWave communication systems provide spatial degree of freedom (DoF) that may be used to enhance main channel to desired users and degrade main channel to Eves. In this way, beam direction may be regulated by the transmitter that can provide best signal-to-noise ratio (SNR) for required users, and confirms least information leakage towards Eves [7]. It is very important to note that Eve with multiple antenna can experience significant information leakage [8].
To enhance the secrecy rate that is considered as the minimal discrepancy between the achievable rate of the required and Eve channel [9], transmitter generates and transmits the artificial noise (AN) in all directions excluding required users. Therefore, it is likely possible that Eve will encounter AN along with desired signals that lessens the SNR at Eve, and makes it tough for it to decode the original signals [10].
An effective directional precodingdesign, known as antenna subset modulation (ASM), is firstly given in [11] for ELEKTRONIKA IR ELEKTROTECHNIKA, ISSN 1392-1215, VOL. 26, NO. 4, 2020 mmWave communication systems. In this scheme, a protected mmWave link is realized by utilizing the specific subset ofantenna array, which helps to develop tightly identified constellation in the aimed angle while randomized constellation in the rest of sides. The ASM approach faces certain computational and side-lobe complications, which are improved by [12]. Authors in [13] developed an effective scheme for secure transmission where Alice (i.e., transmitter) utilizes hybrid massive MIMO schemes with suitable arbitrary approaches to activate a huge number of dumb antennas. This scheme can overcome the eavesdropping capability of Eve and approve itself as a secure scheme against Eves. However, Eve cannot deploy same number of antennas as Alice in this scheme. In [14], authors investigated secure hybrid beamforming scheme for mmWave communication systems. In this scheme, Eve is also deploying the same number of antennas similar to Alice and modeled hybrid-precoding design with high-resolution PSs, and then they presented a hybrid precoder design exploiting low-resolution PSs in [15]. In addition, they obtained secure analog precoder and combiner by utilizing the proposed algorithm, and then found the digital precoder that helped them to further improve the security. However, at higher SNR values, a notable gap is realized between the algorithm reported in [15] and the full-digital benchmark in the study. This fact motivated us to improve the secrecy rate in high SNR regimes.
To the best of our knowledge, no significant work has been done so far to improve thereof gap in high SNR value for mmWave massive MIMO systems using secure hybrid precoder designs. Inspired from [14] and [15], we have two aims in this study. First, is to design a secure hybrid precoder that ensures secure transmission for the intended user without significant information leakage towards Eve, and the second is to improve the secrecy rate at high SNR values in mmWave MIMO communication systems. The primary objective of this work is to intensely examine the secure hybrid precoding algorithms over broadly used scatterer-sharing channel model [16]. The most popular zero-forcing scheme [17] is applied on Eve channel in order to suppress it at eavesdropper side and attempts to reduce the information leakage towards Eve. Later on, we attained secure analog precoder and combiner using the algorithm proposed in this study and the recent algorithm reported in [15]. Finally, digital precoder and combiner are obtained using singular value decomposition (SVD) in this study. It is verified via extensive simulation studies that our proposed algorithm dominates the recent algorithm reported in [15] at high SNR values, while provides similar secrecy rates at low SNR values.
Notations: The lower case, boldface lower case, and boldface upper case letters denote scalars, column vectors, and matrices, respectively. The set of complex numbers is indicated by . The where b y is handled by hybrid combiner ,, . .
Since Eve is also involved in the

A. Secrecy Analysis
The secrecy rate using full-digital precoder and combiner structure is examined by the authors in [15]. They established that the generalized eigen decomposition (GED) scheme [18] based on PLS displays comprehensive outcomes than generalized SVD (GSVD) approach [19] in the mmWave communication systems.Farther, they showed that significant information leakage can be realizable by adopting conventional precoding design without PLS effort, which approves the importance of PLS. Therefore, GEDbased PLS scheme is adopted as performance criteria all over this paper. The analysis of secrecy rate is usually investigated by exploiting the following PLS performance metric: , , , ,

B. Secure Hybrid Precoder Scheme
The hybrid precoder and combiner design problem based on PLS can be defined as follows: ELEKTRONIKA IR ELEKTROTECHNIKA, ISSN 1392-1215, VOL. 26, NO. 4, 2020 where P and C control the resolution of F A and , , Ab W respectively, given in (15) , .
However, still it is a complex hybrid precoder design problem that is resolved into two stages.In first stage, analog precoder and combiner are calculated using proposed algorithm. Then, calculating F D and , W Db using SVD process based on an effective digital channel implemented for Alice, Bob, and Eve. In the following simulation studies, the secrecy rate of our hybrid precoder is examined through the mentioned algorithms in low and high SNR regimes. Typically, we considered 20 dB as threshold value for defining the low and high SNR regimes for ease. The full-digital precoder based on GED scheme with PLS effort will serve as upper bound while hybrid precoder using the spatially sparse precoding (SSP) [20] without PLS will act as lower bound. b R and e R indicate the secrecy rate of Bob and Eve, respectively.
The secrecy rate comparison of proposed algorithm and algorithm reported in [15] is shown in Fig. 2, where we considered the worst scenario by assuming 2 s RF NN  conditions. The outcomes of Fig. 2 clearly demonstrate that the our algorithm achieves performance gain of almost 9 bps/Hz than the SSP. On the other hand, approximately 5.5 bps/Hz of performance gain is obtained by algorithm reported in [15] as compared to SSP. The use of the proposed algorithm provides better results than its counterpart in worst scenario, i.e., around 3.5 bps/Hz enhancement in secrecy. Figure 3 shows spectral efficiency of the hybrid precoders About 38.6 bps/Hz secrecy performance gain is presented by the proposed algorithm as compared to SSP. In contrast, almost 30.7 bps/Hz gain is obtained by the algorithm reported in [15] than SSP that also approves that use of proposed algorithm presents better secrecy rate performance of approximately 8 bps/Hz than the algorithm reported in [15]. It is also noticed that the proposed algorithm achieves nearly 64.5 bps/Hz secrecy performance gain while algorithm reported in [15] attains performance gains of almost 56.5 bps/Hz , which further confirms that the proposed algorithm provides superior secrecy rate performance than its counterpart at high SNR values.
As a final remark, it can be confirmed through the results presented from Fig. 2 to Fig. 4, the proposed algorithm demonstrates remarkable performance improvement in terms of protecting legitimate information from the eavesdropping than that of its counterparts.

V. CONCLUSIONS
Although the use of larger quantization bits guarantees a better analog precoder, it is impractical in mmWave communication systems owing to circuit complexity and high-energy consumptionissues. This paper presented the secrecy rate analysis of various approaches exploiting secure hybrid precoder and combiner in mmWave MIMO communication systems using low-resolution PSs. The extensive simulation studies clearly showed that the proposed algorithm offers approximately 8 bps/Hz better secrecy rate performance at high SNR values than the recently proposed algorithm, and it also exhibits same results with the compared algorithm at low SNR values. Furthermore, the proposed algorithm assures the minimum information leakage towards the Eve when compared to its counterparts, and it is able to provide more protected communication even in worse scenario.

CONFLICTS OF INTEREST
The authors declare that they have no conflicts of interest.