## 2 System Model  
The frame structure in 802.11p consists of a preamble that contains 10 symbols, each one lasting 1.6 us, found at the beginning of the frame and used to synchronize the system. Subsequently, two long training symbols are transmitted, each one lasting 6.4 us, used for fine synchronization and channel estimation. The remaining part of the frame, which has a variable length, is used to transmit the payload. Depending on the different modulation and coding schemes used, IEEE 802.11p permits a number of data transmission speeds ranging from 3 to 27 Mbps [22]. The physical layer of 802.11p, shown in Figure 1, uses 64 subcarriers per OFDM symbol, including 48 data subcarriers, 4 pilot subcarriers located at the indexes \([-21,-7]\), \([7,21]\), 11 virtual subcarriers, and one subcarrier for direct current (DC) component. Let \(x^{k}[n]\) the \(k\)-th transmitted OFDM symbol of \(N_{b}=N+N_{S}\) samples, where \(N\) and \(N_{S}\) are the number of subcarriers and the length of the cyclical prefix (CP), respectively. Assuming that the CP is long enough to absorb the channel impulse response (CIR), the  
Figure 1: Pilot pattern in an 802.11p OFDM frame. \(k\)-th received symbol \(y^{k}[n]\) after removing CP can be expressed in its complex baseband representation as:  
\[y^{k}[n]=\sum_{l=0}^{L-1}h^{k}[n,l]x^{k}[(n-l)_{N}]+w^{k}[n], \tag{1}\]  
where \(n=\{0,...,N-1\}\), \(l=\{0,...,L-1\}\), \(L\) denotes the CIR length, \(h[n,l]\) is the CIR for the \(k\)-th block in the \(n\)-th time instant for an impulse function introduced \(l\) samples earlier, and \(w[n]\) is the circular and symmetrical additive white Gaussian noise (AWGN), with zero mean and variance \(\sigma_{w}^{2}=N_{0}/2\). The circular convolution between the CIR and \(x^{k}[n]\) can be rewritten in matrix form as:  
\[\mathbf{y}^{k}=\mathbf{H}^{k}\mathbf{x}^{k}+\mathbf{w}^{k} \tag{2}\]  
where  
\[\mathbf{y}^{k} =\big{[}y^{k}[0]\quad y^{k}[1]\quad\cdots\quad y^{k}[N-1]\big{]} ^{T},\] \[\mathbf{x}^{k} =\big{[}x^{k}[0]\quad x^{k}[1]\quad\cdots\quad x^{k}[N-1]\big{]} ^{T},\] \[\mathbf{w}^{k} =\big{[}w^{k}[0]\quad w^{k}[1]\quad\cdots\quad w^{k}[N-1]\big{]} ^{T};\]  
in addition, \(\mathbf{H}^{k}\) is an \(N\times N\) matrix, indexed \(0,1,...,N-1\) on each dimension, whose elements are formed with the CIR coefficients as follows:  
\[\Big{[}\mathbf{H}^{k}\Big{]}_{n,n^{\prime}}=h^{k}\big{[}n,(n-n^{\prime})_{N} \big{]}, \tag{3}\]  
where \(n,n^{\prime}=\{0,1,...,N-1\}\) and CIR is assumed to be zero for \(\left(n-n^{\prime}\right)_{N}>L-1\). The OFDM symbol received in frequency domain (FD) is obtained by multiplying both sides of (2) by the matrix of the normalized discrete Fourier transform (DFT):  
\[[\mathbf{F}]_{n,n^{\prime}}=\frac{1}{\sqrt{N}}e^{(-j2\pi nm^{\prime}/N)}, \tag{4}\]  
which gives the result:  
\[\mathbf{u}^{k}=\mathbf{F}\mathbf{H}^{k}\mathbf{x}^{k}+\mathbf{z}^{k}, \tag{5}\]  
where \(\mathbf{u}^{k}\) is the DFT of the \(\mathbf{y}^{k}\) and \(\mathbf{z}^{k}\) is the DFT of noise sequence. Since matrix \(\mathbf{F}\) is unitary, Equation (5) can be expressed as:  
\[\mathbf{u}^{k}=\mathbf{G}^{k}\mathbf{s}^{k}+\mathbf{z}^{k}, \tag{6}\]  
where \(\mathbf{s}^{k}=\mathbf{F}\mathbf{x}^{k}\) is the OFDM symbol transmitted in the frequency domain, consisting of the \(\mathbf{\chi}\) data vector with \(N_{D}\) data symbols, the \(\mathbf{s}_{\mathcal{P}}\) pilot vector with \(N_{P}\) pilots symbols, and \(N_{G}\) guard symbols. \(\mathbf{G}=\mathbf{F}\mathbf{H}\mathbf{F}^{H}\) is the channel frequency matrix (CFM). When the Doppler propagation is insignificant, \(\mathbf{G}\) is a diagonal matrix, and the system is ICI-free. In V2V environments, due to high mobility of both the transmitter and the receiver, the combined effect of Doppler shift for each of the individual received paths results in significant Doppler dispersion, causing the CIR to become time varying within an OFDM symbol and resulting in matrix \(\mathbf{G}\) to have energy on the components outside of the diagonal, giving rise to ICI.