## 2 System Model  
We consider an MISO system consisting of \(N_{t}\) sending antennas and a single receiving antenna in a slightly static spatially correlated Nakagami m-fading channel scenario. We do this by implementing a new transmitter scheme that combines quasi-orthogonal space-time block coding (QQSTBC) with recently proposed generalized quadrature spatial modulation (GQSM) [14]. In this system, out of all the \(N_{t}\) antennas, a variable number, \(p\), of the transmitting antennas are turned on. Through the use of antenna activation permutation (AAP), the actual component of the modulated signal vector (\(I^{I}\)) can be sent through activated antennas. Similarly, an alternate AAP is used for activated antennas to transmit the imaginary component (\(I^{Q}\)) of the modulated signal vector. The total AAPs for the real and imaginary components are denoted by \(C(N_{t},p)\). Specifically, \(L=2^{\lfloor log_{2}C(N_{t},p)\rfloor}\) is the AAP of the modulated signal vector. In this case, \(C(N_{t},p)\) represents the process of identifying \(p\) antennas from collection of \(N_{t}\) antennas. We then describe the transmission and detection of GQSM. The entire set of given input bits (\(\mathbf{m}\)) was divided after the data was separated into \(\mathbf{m}_{1}\), \(\mathbf{m}_{2}\), and \(\mathbf{m}_{3}\). The binary components that modulate M-ary are described by \(\mathbf{m}_{1}\), which results in a signal-modulated vector \(\mathbf{s}\) with elements \(s_{1},s_{2},\ldots,s_{p}\). With \(\mathbf{m}_{1}=p\cdot\log 2(M)\) bits, the starting vector \(\mathbf{s}\) is created. For \(1\leq\tau\leq p\), each of the components \(s_{\tau}\) in the vector is represented as \(s_{\tau}=s_{\tau}^{I}+js_{\tau}^{Q}\). \(s_{\tau}\) is a member of the set \(\chi\), which is made up of \(M\) -ary constellation points. Importantly, \(s_{\tau}^{Q}\) with \(s_{\tau}^{I}\) are taken from \(\chi^{Q}\) and \(\chi^{I}\), which represent both the imaginary and the real components of \(\chi\), respectively. The bits \(\mathbf{m}_{2}\) and \(\mathbf{m}_{3}\) represent the index bits of the real and imaginary components, respectively. The bits of \(\mathbf{m}_{2}=\lfloor log_{2}C(N_{t},p)\rfloor\) are used to calculate the AAPs of \(I^{I}\) and \(\mathbf{m}_{3}=\lfloor log_{2}C(N_{t},p)\rfloor\). \(\{s_{\tau}^{I}\}_{\tau=1}^{p}\) and \(\{s_{\tau}^{Q}\}_{\tau=1}^{p}\) are signals that use bits to represent the AAPs of \(I^{Q}\) to transmit their real and imaginary parts. Example: Four \(N_{t}\) = four \(p\) = two and 4-QAM \((M=4)\): As per the equation \(\mathbf{m}_{1}=log_{2}M\), there are four 4-QAM modulation bits. There are two AAP real bits in \(\mathbf{m}_{2}\) and two AAP imaginary bits in \(\mathbf{m}_{3}=\lfloor log_{2}C(N_{t},p)\rfloor\). Consequently, there are eight bits in all. The data input bits for \(\mathbf{m}\) are now [0 1 1 0 1 1 0 0]. The system model states that the first 4 (\(\mathbf{m}_{1}=4\)) bits [0 1 1 0] are turned into 2 (\(p=2\)) modulated characters \(\mathbf{s}=[-1+j,1-j]\) with \(\mathbf{s}^{l}=[-1,1]\) and \(\mathbf{s}^{Q}=[1,-1]\). The middle or second two (\(\mathbf{m}_{2}=2\)) bits [1 1] are used to opt the AAP \(I_{4}^{I}=\{2,3\}\) (refer to Table 1) to transmit \(s_{1}^{I}=-1\) and \(s_{2}^{I}=1\) via the second (\(i_{4}^{I}(1)=2\)) and third (\(i_{4}^{I}(2)=3\)) antennas for the real part of \(\mathbf{s}\), leading to \(\mathbf{x}^{I}=[0,1,1,0]^{T}\). The third or last two (\(\mathbf{m}_{3}=2\)) bits [0, 0] are used to select the AAP \(I_{1}^{Q}=\{1,2\}\) (refer to Table 1) to transmit \(s_{1}^{Q}=1\) and \(s_{2}^{Q}=-1\) through the first (\(i_{1}^{Q}(1)=1\)) and second (\(i_{1}^{Q}(2)=2\)) antennas, resulting in \(\mathbf{x}^{Q}=[1,1,0,0]^{T}\). Thus, \(\mathbf{x}=\mathbf{x}^{I}+\mathbf{x}^{Q}=[j,-1-j,1,0]^{T}\) yields the transmitted signal vector. Let \(\mathbf{s}^{I}\) denote the real components of the modulated signal vector \(\mathbf{s}\), which is denoted as \([s_{1}^{I},s_{2}^{I},\ldots,s_{p}^{I}]\).