# Efficient MIMO Signal Predistortion for Secrecy-Enhancing
## 1 Introduction  
The multi-input multi-output (MIMO) scheme is one of the most representative technologies in modern wireless communication systems, including wireless LAN as well as 4G to beyond 5G systems. To date, most of the physical layer technologies for MIMO systems have prioritized performance and capacity issues over security protection. However, dramatically increasing traffic demands, especially of machine-type communications, require more secure communication for privacy protection. Therefore, a number of studies have emphasized the importance of physical layer security (PLS) schemes for modern wireless communication systems [1, 2], and there have been many proposals concentrating on the signal design for MIMO systems [3, 4, 5, 6, 7, 8, 9, 10, 11]. Techniques to add artificial noise (AN) have been considered as an effective means to protect the legitimate channel [3, 4, 5, 6, 7, 8]. A typical design principle of AN is to make it orthogonal to the legitimate channel, so that it can be null to the legitimate receiver, while serving as interference to the illegal receiver [3]. Then, this idea of adding AN was applied to spatial modulation and space time block coding (STBC) schemes in [4, 5, 6, 7, 8], respectively, for PLS. However, adding AN obviously requires additional energy, which decreases the energy efficiency. Because of this, a recent study proposed the idea of adding artificial interference (AI), which can be considered as the channel dependent re-distribution of signal power, and this, therefore, accomplishes security protection without requiring any additional energy [9]. All of these ideas of adding AN or AI utilize the addition or re-distribution of channel-dependent power at the transmitter, which results in a seriously high peak-to-average power ratio (PAPR) problem. To avoid the high PAPR problem, ideas that involve distorting the phase of the complex signal have been proposed [10, 11]. For example, a phase rotation method has been appliedto the STBC schemes to enhance secrecy [10], but the randomness of the phase distortion to the eavesdropper is only guaranteed by the additional secret key exchange between the legitimate transmitter and receiver. Meanwhile, a phase rotation technique was applied to the spatial modulation scheme to increase secrecy performance without risking any PAPR problem [11]. In these schemes, the secrecy protection capability is limited by the number of antennae and the modulation order employed. In this paper, we propose novel secrecy enhancing methods for MIMO schemes. We consider that full-rate orthogonal STBC (O-STBC) schemes exist for instances employing more than two transmit antennae when real-numbered signals are used [12]. The proposed scheme first forms a full-rate non-orthogonal STBC encoding matrix, and then applies signal distortion for PLS in such a way as to make the channel matrix at the receiver fully orthogonal. Therefore, we can have a full-rate encoding matrix at the transmitter and a fully orthogonal channel matrix at the receiver. In addition to high secrecy protection, this leads to high performance gain due to higher diversity gain than the conventional methods. By extending this to the spatial multiplexing (SM) MIMO scheme, we design a new predistortion scheme. The main contributions of this paper compared to the conventional schemes can be summarized as follows:  
* Compared to the conventional AN or AI-aided schemes [3; 4; 5; 6; 7; 8; 9], the proposed methods distort the phase of the transmit signal, and they therefore avoid the PAPR problem and do not require additional energy for AN. * Compared to the conventional phase-distortion based schemes [10; 11], the proposed methods do not require an additional secret key exchange and have no limit on the secrecy protection capability. * Compared to the conventional STBC schemes [12; 13; 14; 15], the proposed scheme not only provides better bit error rate (BER) performance at the same rate (or can achieve the same performance at a higher rate), but it can also achieve high security protection.