# A Review of Physical Layer Security Techniques for Internet of Things: Challenges and Solutions
## 2 Literature Review of PLS Techniques for IoT  
### Information-Theoretical Fundamentals of Physical Layer Security  
The research of physical layer security can be traced back to the secret communications theory established by [PERSON] [11]. According to [PERSON]'s theory, the system is considered to be in perfect secrecy if the following condition is satisfied:  
\[H(M|X)=H(M), \tag{1}\]  
where \(H(M)\) and \(H(M|X)\) are the entropy of the message \(M\) and the conditional entropy of \(M\) conditioned on eavesdropper's observation \(X\), respectively. To achieve perfect secrecy, the code that is used to encode the message must be independent of the message itself. One feasible approach to realize this is the \"one-time pad\" encryption, where each secret-key bit is XORed with each message bit to produce the transmitted codeword \(X\). This requirement is too demanding in many applications. Unlike [PERSON]'s work, [PERSON] proposed a noisy wiretap channel model in 1975 [12]. The noisy wiretap channel is composed of one legitimate transmitter ([PERSON]), one legitimate receiver ([PERSON]), and one eavesdropper ([PERSON]). For this model, [PERSON] formulated the condition for secure transmission, i.e., the transmission is information-theoretically secure if the decoding error probability at the legitimate receiver can be arbitrarily small while no source information can be obtained by the eavesdropper. The maximum rate under which the above condition can be met is termed as the secrecy capacity, which characterizes the performance limits for secure transmissions in noisy channels. In Gaussian wiretap channels, the secrecy capacity \(C_{s}\) equals the difference in the Shannon capacities between the legitimate (Alice-Bob) link and the eavesdropping (Alice-Eve) link, i.e.,  
\[C_{s}=\left[\log(1+\text{SNR}_{\text{B}})-\log(1+\text{SNR}_{\text{E}})\right] ^{+}, \tag{2}\]  
where \([x]^{+}=\max(x,0)\), and \(\text{SNR}_{\text{B}}\) and \(\text{SNR}_{\text{E}}\) are the received signal-to-noise ratios (SNRs) at Bob and Eve, respectively. Based on Label (2), the keyless secure communications can be realized as long as the channel quality of the legitimate link is advantageous over that of the eavesdropping link. Therefore, Ref. [12] laid the foundation for the PLS technique research. However, throughout the long period since the publication of [PERSON]'s work, the PLS technique has not attracted much attention. This is attributed to the following reasons: first, the achievability of the secrecy capacity relies on the use of stochastic coding. However, it is extremely difficult to construct practical stochastic codes with affordable complexity. Second, in order to achieve the positive secrecy capacity, the received SNR at the legitimate user must be strictly higher than that at the eavesdropper, which is hard to be guaranteed in wireless environments. Last but not the least, shortly after the concept of secrecy capacity was proposed, [PERSON] and [PERSON] devised the public-key cryptography, which relies on mathematical functions believed hard to compute and has dominated security research since its appearance. Due to the above reasons, the research of information-theoretical security touched a low point in the 1970s-1980s. During that period, the representative outcomes in the area of information-theoretic security mainly include [13; 14]. To be specific, [PERSON]. [13] analyzed the secrecy capacity for the physically degraded Gaussian wiretap channel, and Ref. [14] generalized [PERSON]'s results to broadcast channels. Since the 1990s, with the widespread applications of wireless communications techniques and the increasing popularity of wireless services, the security issue of wireless networks is becoming more and more important, which reignites the research interests in information-theoretical security. In this context, significant advances have been achieved in information-theoretical security studies, mainly including the secrecy capacity analysis for various network models. Ref.