# A W-Band Communication and Sensing Convergence System Enabled by Single OFDM Waveform
## 4 Simulation Results  
To verify the processing of the proposed OFDM-based converged system, a baseband equivalent model is implemented and simulated in MATLAB. An impulse response, having taps at the round-trip delay of the targets, and each tap varying over OFDM symbols according to the complex exponential of the Doppler frequency, is used to represent the sensing channel, whereas \(\text{SNR}=15\) dB is set for simulation. Equal signal strength is used for different targets, while other parameters, listed in Table 2, are selected to match parameters used in our experiment. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**OFDM-Based Sensing**} & \multicolumn{2}{c}{**Proposed Method**} \\ \hline
**Operation** & **Complex** & **Complex** & **Operation** & **Complex** & **Complex** \\  & **Multiplications** & **Additions** & **for Q\(N_{\text{s}}\) Delays** & **Multiplications** & **Additions** \\ \hline Division to get \(\mathbf{H}\) & \(4 MN_{ac}\) & 0 & Division to get \(\mathbf{H}\) & \(4 MN_{ac}Q\)\(N_{\text{s}}\) & 0 \\ \hline \(N\)-point IFFT & \(M(N/2)\log_{2}(N)\) & \(MN\log_{2}(N)\) & \(N\)-point IFFT & \((Q\)\(N_{\text{s}})\)\(M\)\((N/2)\log_{2}(N)\) & \((Q\)\(N_{\text{s}})\)\(MN\)\(\log_{2}(N)\) \\ \hline \(M\)-point FFT & \(N(M/2)\log_{2}(M)\) & \(MN\log_{2}(M)\) & \(M\)-point FFT & \((Q\)\(N_{\text{s}})\)\((M/2)\log_{2}(M)\) & \((Q\)\(N_{\text{s}})\)\(M\)\(\log_{2}(M)\) \\ \hline Total & \((MN/2)\log_{2}(MN)\) & \(MN\log_{2}(MN)\) & Total & \((Q\)\(N_{\text{s}})\)\((M/2)\)\((N\log_{2}(N)\) & \((Q\)\(N_{\text{s}})\)\(M\)\((N\log_{2}(N)\) \\  & & & & \(+\log_{2}(M))\) & \(+\log_{2}(M))\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Computational complexity of the proposed method. \begin{table}
\begin{tabular}{c c} \hline \hline Sampling frequency \(F_{\text{s}}\) & 6 GHz \\ \hline Carrier frequency \(f_{\text{c}}\) & 97 GHz \\ \hline FFT size \(N\) & 512 \\ \hline Subcarrier spacing \(\Delta f\) & 11.71875 MHz \\ \hline No. of active subcarriers \(N_{\text{ac}}\) & 300 \\ \hline Bandwidth \(B\) & 3.9 GHz \\ \hline Bandwidth occupied by active subcarriers & 3.51 GHz \\ \hline Bandwidth utilization & 90\% \\ \hline Digital mapping & 16 QAM \\ \hline Effective OFDM symbol duration \(T_{\text{s}}\) & 0.1066 \(\upmu\)s \\ \hline Cyclic prefix duration (CP) & 128 samples, 0.0213 \(\upmu\)s \\ \hline No. of OFDM symbols \(M\) & 36 for range \\  & 18,432 for speed \\ \hline Range resolution \(\Delta R=c/(2\Delta f/N_{\text{ac}})\) & 0.042 m \\ \hline Unambiguous range \((N-1)c/(2\Delta fN)\) & 12.775 m \\ \hline Maximum range (within CPI) & 3.2 m \\ \hline Speed resolution \(\Delta\
u\) & 0.79 m/s \\ \hline Unambiguous speed \(\pm\frac{(M-1)\Delta\
u}{2}\) & \(\pm\)7464 m/s \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters. It is important to note that for scenarios where we use only static targets, \(M=36\) is used, which provides sufficient gain for range detection but results in a high value of \(\Delta v\) in the range/speed plot, although this is irrelevant for static targets. For the range/speed plot, the absolute of the delay/Doppler matrix is first normalized to unit (by dividing with the maximum absolute value) and then converted to dB scale. Figure 4a-c presents the range plots for static targets at distances 0.6 m, 1.3 m 1.5 m, and 10 m, respectively, using the conventional OFDM-based sensing. Results show that the targets are identified correctly at the distances in Figure 4a,b. However, Figure 4c clearly shows that the sensing performance has been compromised, in terms of SNR, for the target located at a 10 m distance.