# Secrecy Enhancing Scheme for Spatial Modulation Using Antenna Selection and Artificial Noise
## 2 PLS Scheme with SM  
Figure 1 shows a system model using SM for PLS. In the generic model of the PLS scheme, there is a cooperative wireless network consisting of three nodes, as shown in Figure 1. One source node, which is the legitimate transmitter node, is referred to as Alice. The corresponding destination  
node is referred to as Bob, which is the legitimate receiver node. On the other hand, the third node, named [PERSON], is the passive eavesdropper node. In this model, [PERSON] sends the secret data sequence and communicates confidentially with [PERSON]. [PERSON] attempts to intercept the ongoing communication between the legitimate link, i.e., from the transmitter [PERSON] to the legitimate receiver [PERSON]. In other words, [PERSON] tries to decode and obtain the secret data content from her own observations of the received signals [9].  
As shown in Figure 1, it is assumed that the transmitter Alice is equipped with \(N_{t}\) antennas, and \(M\)-ary amplitude and phase modulation (APM) symbols are transmitted over one of the \(N_{t}\) antennas at each signaling time instance. The channels from [PERSON] to [PERSON] and [PERSON] are represented by the \(N_{Rb}\times N_{t}\) matrix \(\mathbf{H}\) and \(N_{Re}\times N_{t}\) matrix \(\mathbf{G}\), respectively, where \(N_{Rb}\) and \(N_{Re}\) are the numbers of receive antennas at [PERSON] and [PERSON], respectively. All the channel gains for each transmitted symbol, i.e., all the elements of \(\mathbf{H}\) and \(\mathbf{G}\), are assumed to be independent complex Rayleigh random variables and not to have frequency selectivity. The number of transmit antennas, \(N_{t}\), in the conventional SM system is usually assumed to be a power of two [1]. At the transmitter, the bit stream emitted by a binary source is divided into blocks containing \(n_{t}\) and \(\ell\) bits each, where \(n_{t}=\log_{2}N_{t}\) is the number of bits to identify a transmit-antenna among \(N_{t}\) antennas, and \(\ell=\log_{2}M\) is the number of bits in an \(M\)-ary symbol. Therefore, the effective data rate \(r_{e}=n_{t}+\ell\).  
When a symbol is chosen to be transmitted at the \(j\)-th antenna among \(N_{t}\) antennas, the transmission from Alice can be represented by the \(N_{t}\times 1\) column vector, \(\mathbf{x}\), as follows [14]:  
\[\mathbf{x}=[0\ldots 0\underbrace{x_{m}}_{j-th}0\ldots 0]^{T}=\mathbf{e}_{j} \cdot x_{m}, \tag{1}\]  
where \(x_{m}\) denotes a modulation symbol drawn from \(M\)-ary APM constellation whose power is normalized to one and \(\mathbf{e}_{j}\) is a unit vector whose \(j\)th entry is non-zero for \(j\in\{1,2,\cdots,N_{t}\}\). Then, the received signal vector \(\mathbf{y}_{b}\in\mathbb{C}^{N_{Rb}\times 1}\) at Bob and \(\mathbf{y}_{e}\in\mathbb{C}^{N_{Re}\times 1}\) at Eve are represented by:  
\[\mathbf{y}_{b}=\mathbf{H}\mathbf{x}+\mathbf{n}_{b}=\mathbf{h}_{j}x_{m}+\mathbf{ n}_{b}, \tag{2}\]  
and:  
\[\mathbf{y}_{e}=\mathbf{G}\mathbf{x}+\mathbf{n}_{e}=\mathbf{g}_{j}x_{m}+ \mathbf{n}_{e}, \tag{3}\]  
Figure 1: Physical layer security scenario for the spatial modulation systems.  
respectively. In the above equations, \(\mathbf{h}_{j}\) and \(\mathbf{g}_{j}\) are the \(j\)th column vectors of \(\mathbf{H}\) and \(\mathbf{G}\), respectively, and \(\mathbf{n}_{b}\in\mathbb{C}^{N_{R\oplus}\times 1}\) and \(\mathbf{n}_{e}\in\mathbb{C}^{N_{R\oplus}\times 1}\) denote the complex additive white Gaussian noise (AWGN) vectors.