## 3 System Model
### OFDM-IM Communication Transmission Framework  
The block diagram of the OFDM-IM transceiver module model for vehicular communication is illustrated in Figure 2. As shown in this figure, Module A denotes the bit demultiplexer, Module B denotes index selection, Module C denotes constellation mapping, Module D denotes the OFDM block generator, Module E denotes the N-point inverse fast Fourier transform (IFFT), Module F denotes cyclic prefix (CP) addition, Module G denotes CP removal and analog-to-digital conversion, Module H denotes the N-point FFT, Module I denotes signal decomposition, Module J denotes index demodulation, Module K denotes inverse index mapping, Module L denotes M-order demodulation, and Module M denotes parallel-to-serial conversion. At the transmitter, each OFDM symbol employs \(U\) subcarriers to transmit a total of \(B\) bits. These \(B\) bits are then divided into \(G\) groups, each containing \(p\) bits, which gives \(B=pG\). For each group, \(K\) bits are mapped to an OFDM subblock of length \(N\), where \(N=U/G\), and \(U\) also denotes the size of the fast Fourier transform (FFT). Unlike traditional OFDM, in each subblock, only \(K\) out of the \(N\) subcarriers are activated and used for constellation symbol transmission. These \(K\) subcarriers are termed active subcarriers, while the remaining \((N-K)\) subcarriers are inactive. The \(p\) bits within each subblock are divided into two parts: \(p_{1}\) bits are used to control the positions of the active subcarriers, while \(p_{2}\) bits are used for traditional signal constellation mapping. For each subblock, the input \(p_{1}\) bits are transmitted to the index selector. The index selector selects \(K\) active indices from \(N\) available indices based on a predetermined index selection scheme. The selected indices can be expressed as  
\[I_{\beta}=\big{\{}i_{\beta,1},i_{\beta,2},i_{\beta,3},\ldots,i_{\beta,K}\big{\}}. \tag{13}\]  
Among them, \(i_{\beta,k}\in[1,2,3,\ldots,N]\), \(\beta=1,2,3,\ldots,G\) and \(k=1,2,3,\ldots,K\). The number of bits carried by the positions of active indices in the subblock is \(p_{1}=\big{\lfloor}\log_{2}C_{N}^{K}\big{\rfloor}\). The input \(p_{2}\) bits are transmitted to an \(M\)-bit modulator and mapped to the \(M\)-bit signal constellation, determining the modulation symbols carried by the \(K\) active subcarriers. The output of \(M\)-order constellation modulation is given by  
\[S_{\beta}=\big{[}s_{\beta,1},s_{\beta,2},\ldots,s_{\beta,k},\ldots,s_{\beta,K }\big{]}, \tag{14}\]  
where \(s_{\beta,k}\in\Omega\) and \(\Omega\) represent the set of \(M\)-order constellation signals. Assume that the signal constellation is normalized to unit average power, meaning \(E\big{\{}S_{\beta}S_{\beta}^{H}\big{\}}=K\). The  
Figure 2: Block diagram of transmitter and receiver modules. number of information bits carried by the \(M\)-order constellation symbols is \(p_{2}=\text{Klog}_{2}M\). The output of the \(\beta\)th OFDM-IM subblock generator is given by  
\[\mathbf{X}_{\beta}=\big{[}x_{\beta}(1),x_{\beta}(2),\ldots,x_{\beta}(n),\ldots x _{\beta}(N)\big{]}^{T}, \tag{15}\]  
\[x_{\beta}(n)=\left\{ \begin{array}{l}s_{\beta,n},n\in I_{\beta}\\ 0,\text{otherwise}\end{array} \right., \tag{16}\]  
where \(n=1,2,\ldots,N\). The OFDM-IM subblock generator takes into account \(I_{\beta}\) and \(S_{\beta}\) for each subblock. After generating all OFDM-IM subblocks, these subblocks are combined into an \(U*1\)-dimensional OFDM-IM block. \[\mathbf{X}_{F}=[x(1),x(2),\ldots,x(u),\ldots,x(U)]^{T}. \tag{17}\]  
To counteract channel fading, \(x(u)\in\{0,\Omega\}\), \(u=1,2,\ldots,U\) can apply block interleaving to \(\mathbf{X}_{F}\), resulting in an interleaved OFDM-IM block, \(\widetilde{\mathbf{X}}_{F}\). Then, \(\widetilde{\mathbf{X}}_{F}\) can be converted to the time domain using an IFFT.