# Novel Sparse-Coded Ambient Backscatter Communication for Massive IoT Connectivity
## 5 Simulation Results
### Applicability to M-Ary Modulation  
Figure 8 shows the effect of the modulation order \(M\) on the harvesting probability and the conditional BER. In a conventional TD-AmBC modulator, the harvesting probability is irrelevant to the value of \(M\), since all the \(M\)-PSK symbols are on the circle of radius \(\sqrt{\alpha}\) as shown in Figure 3(a) with \(\beta=0.25\alpha,\forall M\) in (7). Note that the reflection coefficient \(\alpha\) in the horizontal axis is related to SNR per symbol rather than SNR per bit. Consequently, as \(M\) increases, conditional BER in TD-AmBC degrades as the SNR per bit is reduced by factor \(\frac{1}{\log_{2}M}\)[22].  
On the other hand, in an SC-AmBC modulator, the harvesting probability is affected by the modulation order \(M\) and the backscatter power \(\sigma_{b}^{2}\) in (13), which can be analyzed by the value of \(\beta\) and the threshold \(\theta\) in (8). In 2-ary modulation, the normalized energy per symbol is given by \(\beta=0.5\alpha\), which is larger than those in TD-AmBC modulations. Larger value of \(\beta\) increases the threshold value \(\theta\) and eventually reduces the harvesting probability. Similarly, we can anticipate the performance degradation in 8-ary modulation with \(\beta=0.375\alpha\). However, we can observe no performance degradation, especially for 4-ary modulation. In the 4-ary SC-AmBC, the duty cycle \(D\) is doubled by using spreading sequences with factor \(K_{1}=2\) and the backscatter power \(\sigma_{b}^{2}\) is reduced to half by using zero-constellation point represented in Figure 3(b). As a result, the non-orthogonal signaling with zero symbols (i.e., idle state) in SC-AmBC can compensate the harvesting probability without energy loss.  
In terms of the BER performance in Figure 7(b), all of the SC-AmBC schemes outperform the TD-AmBC schemes. Extension of signal space via sparse coding can enable \(1.5\times\) overloading as well as achieve significant diversity gains. Consequently, it is noted that, for large \(\alpha\), 4-ary SC-AmBC provides even lower BER than 2-ary TD-AmBC with the same \(\beta\). Although the average backscatter power is the same, SC-AmBC can utilize instantaneous channel fluctuations among different time slots,  
Figure 8: Effect of the modulation order \(M\) (\(L^{+}=3\), \(K=4\), \(\lambda=1.5\) for SC-AmBC).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Values** & **References** \\ \hline OFDM signaling & \(\sigma_{s}^{2}=20\) dBm / \(\sigma_{n}^{2}=-90\) dBm / \(T_{s}=50\) ns & IEEE 802.11g [57] \\ \hline Antenna property & \(A_{e}=0.0012\) m\({}^{2}\) / \(G_{s}=+3\) dB & Testbed results [2] \\ \hline Tag hardware & \(\eta=0.25\) / \(\sigma_{c}^{2}=0.58\) pJ/symbol & Testbed results [9; 51] \\ \hline Sparse code & \(K_{1}=2\) / \(N_{l}=3\) iterations & Theoretical results [39] \\ \hline Coverage, rate & \(d=5\) m / \(L=8\) samples & Simulation settings [2] \\ \hline \hline \end{tabular}
\end{table}
Table 3: System parameters.  
achieving modulation diversity [54]. Therefore, the proposed SC-AmBC can support small-form RF devices with \(M\)-ary modulation.