# Clutter-Masked Waveform Design for LPI/LPD Radarcom Signal Encoding
## 5 Clutter-Masked Radarcom Waveform Performance Evaluation
### Clutter-Masked Communication Performance  
After establishing the method's clutter-masking potential, we need to investigate the efficiency of communications. The \(b\)-parameter of the Arcsine distribution was used to encode communication data. Depending on the symbol being sent, the \(b\)-parameter was changed before being used in (8). Upon reception, this parameter was estimated using the relationship between it and the average value of received samples of OFDM sub-carrier amplitudes. This method was tested in simulation, as described below.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**PDF Type** & **MSE** & **NMSE** & **NRMSE** \\ \hline Arcsine (b = 100) & \(3.125\times 10^{-6}\) & \(0.9974\) & \(0.9493\) \\ Arcsine (b = 101) & \(3.933\times 10^{-6}\) & \(0.9967\) & \(0.9429\) \\ Arcsine (b = 99) & \(5.447\times 10^{-6}\) & \(0.9956\) & \(0.9  
First, we created an arbitrary 168-bit binary signal. We assumed that the clutter in the area was described by Equations (8)-(10) where \(b\approx 110\). The mean of this distribution converges to  
\[E[\textbf{W}]=\frac{b}{2}, \tag{12}\]  
where **W** is a vector containing samples of OFDM sub-carrier coefficients from (11) and \(E[\_]\) denotes mathematical expectation, or average value. We then set our \(b\)-parameter for use in radarcom signal generation to a value of 100 for bit value of 0, and to 120 for bit value of 1. An OFDM signal with 32 sub-carriers was generated for each bit using (1) with \(S(m)\) formed as per (11). Upon reception, a friendly platform used FFT to reconstruct the sub-carrier coefficients \(S(m)\) using FFT and extracting the magnitude estimates \(\hat{\textbf{W}}\) only, via the process explained in [5]. Once these estimates were obtained, the value of the \(k^{\text{th}}\) bit \(A_{k}\) was estimated using the vector \(\hat{\textbf{W}}_{k}\) and the estimate of its corresponding \(b\)-parameter as:  
\[\hat{A}_{k}=\left\{\begin{array}{l}0\;if\;\hat{b}_{k}=2E\left[\hat{\textbf{W }}_{k}\right]<55\\ 1\;if\;\hat{b}_{k}=2E\left[\hat{\textbf{W}}_{k}\right]>55\end{array}\right.. \tag{13}\]  
Additive white Gaussian noise (AWGN) was added to the received clutter-masked signals and BER characteristics were computed for various signal-to-noise ratios (SNR). The resultant BER vs SNR plots are shown in Figure 2 for the cases of single transmission, as well as 10, 100, and 300 retransmissions per signal, where each retransmission carries the same bit sequence, but each waveform realization was different thanks to drawing the signal samples from the random distribution as described above. In absence of error control coding, or other improvements, we note that the obtained BER values are higher than those of modern broadband data communication schemes; as pointed out in [5], however, this is due to prioritizing transmission security over BER/throughput. Compared to [12; 13], we note that the proposed scheme has poorer BER below +10 dB, but better bps potential and much stronger LPI/LPD characteristics.  
Figure 2: Bit error rate (BER) vs. signal-to-noise ratio (SNR) for clutter masked communications: (**a**) 1 Retransmission; (**b**) 10 Retransmissions; (**c**) 100 Retransmissions; (**d**) 300 Retransmissions.