## 2 System Model  
The block diagram of the proposed eOFDM is shown in Figure 1. The data source generates a binary sequence of 1s and 0s, which are then modulated using an \(M\)-ary digital modulation scheme. A block of \(M\)-ary symbols is fed to the IFFT block as well as the PN sequence selection (PNSS) block. The unique PNSS block selects one PN sequence from a group of pre-selected sequences. This selection is based on the subset of \(M\)-ary data symbols at specified subcarriers, which is described in subsequent text. The selected PN sequence is then used as a guard interval for the eOFDM block, which is transmitted over wireless channel. AT the receiver, the PN sequence detection and removal (PNSDR) process is completed before the FFT operation. It should be noted that a subset of \(M\)-ary symbols are detected before the FFT operation due to the PNSDR block. _Proposed eOFDM Block Structure_  
The structure of transmitted blocks for CP-OFDM, TDS-OFDM and the proposed eOFDM systems are compared with the help of the illustration in Figure 2. The set of all OFDM subcarriers in a block are indexed, and a set \(B=[1,2,\ldots,N]\) of indices is formed. Set \(B\) can be split into \(G\) groups. There are \(J=N/G\) subcarriers in each set \(B_{g}\subset B\), \(g=1,2,\ldots,G\). The random source, generating uniformly distributed sequence of 1s and 0s as input, are grouped and mapped to complex valued set of symbols \(\mathbf{s}=[s_{1},s_{2},\ldots,s_{N}]^{T}\) chosen from an \(M\)-ary digital modulation scheme, where \((. )^{T}\) represents the transposition operations. Although, in general, any \(M\geq 2\) can be used for data symbols, we select \(M=2\) for the brevity and simplicity of the new idea. Each subset \(B_{g}\) of the subcarriers are used to transmit \(J\) complex valued symbols from \(\mathbf{s}\). The \(N\) point IDFT operation of \(\mathbf{s}\) yields \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Guard Interval Significance** & **Pilot Tones and Flexibility** \\ \hline \multirow{2}{*}{**CP-OFDM**} & Variable CP as GI in each OFDM block & Scattered pilot tones compromises SE; \\  & is used, which removes ISI & simplified but inflexible block structure \\ \hline \multirow{3}{*}{**TDS-OFDM**} & Fixed PN sequence as GI in each & No pilot tones, hence no compromise \\  & OFDM block is used, which removes ISI with additional CE capability & on SE; simplified but inflexible \\ \hline \multirow{3}{*}{**eOFDM**} & Novel variable PN sequence as GI is & No pilot tones, hence, no compromise \\  & used variable PN sequence as GI is & on SE, but nevertheless, a subset of \\ \cline{1-1}  & used, which removes ISI, improves & data symbols can be used as pilot tones \\ \cline{1-1}  & block BER with additional CE & as in CP-OFDM (future extension (FE)) \\ \cline{1-1}  & capability & without any compromise on SE; \\ \cline{1-1}  & & flexible block structure (FE) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of CP-OFDM, TDS-OFDM and eOFDM salient features. \(\mathbf{x}=[x_{1},x_{2},\ldots,x_{N}-1]^{T}\), which is a time domain sequence, where the real valued \(x_{n}\) can be expressed as [31]  
\[x_{n}=\frac{1}{\sqrt{N}}\sum_{k=0}^{N-1}X_{k}^{\prime}e^{j2\pi n\frac{k}{N}},n=0,1,\ldots,N-1 \tag{1}\]  
The guard interval is selected from the set of a well-known PN sequence \(\{\mathbf{x}_{d}\}\), \(d=1,2,\ldots,2^{G}\), which exhibits the constant amplitude and zero cross-correlation properties in the time domain [32; 33; 34; 35]. The unique feature of eOFDM is the selection of \(\mathbf{x}_{d}\), which is based on \(s_{i}\)s carried by the subcarriers with indices from \(B_{o}^{\prime}\subset B\), where \(B_{o}^{\prime}=\{o_{1},o_{2},\ldots,o_{G}\}\) and \(o_{i}\in\{1,2,\ldots,J\}\) for each \(B_{g}\). It should be noted that \(B_{o}^{\prime}\) is formed from the available set of \(N\) subcarriers with only one subcarrier from each \(B_{g}\).