# Multi-Dimensional Sparse-Coded Ambient Backscatter Communication for Massive IoT Networks
## 5 Simulation Results
### Practical Implementation of AmBC  
We evaluated AmBC system in Wi-Fi OFDM networks using 2.4 GHz industrial, scientific and medical (ISM) band and following IEEE 802.11g specifications [45] as depicted in Figure 9b. Specifically, the index set of Wi-Fi OFDM subcarriers can be given by \(\Phi_{\text{PI}}=\{12,26,40,54\}\) (pilot subcarriers), \(\Phi_{\text{G}}=\{1,2,3,4,5,6,33,60,61,62,63,64\}\) (guard subcarriers) and \(\Phi_{\text{D}}=\Phi-(\Phi_{\text{PI}}\cup\Phi_{\text{G}})\) (data subcarriers) where \(\Phi=\{1,2,\cdots,L\}\). Also, the rest of the system parameters [3; 18; 25; 41] can be found in Figure 9b. Although we selected Wi-Fi carriers for performance evaluations, the system can also be generalized to support the other OFDM networks such as LTE or DVB by simple modification of the system parameters (e.g., the pilot subcarrier set \(\Phi_{\text{PI}}\), the CP size \(L_{\text{CP}}\), and the bandwidth \(W\)). Due to the wide availability of OFDM carriers and the sparsity of tags' operations, our AmBC system can be implemented in various IoT applications including smart city, factory and farm where massive IoT connectivity is required to monitor environments and seamlessly provide useful information to the reader for intelligent decision-making for those systems. In these applications, there are \(U\) multiple  
Figure 8: Block diagram of AmBC systems in view of modulation, coding and detection. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Component** & **TD-AmBC** & **MSC-AmBC** \\ \hline
**(1) Modulation** & [3; 17; 18; 19; 20; 21; 22] & \\ \hline Signal constellation & 2-dimensional PSK/QAM & \(K_{1}\geq 2\) dimensional lattice \\ Load impedance & \(M\geq 2\) impedances & \(\bar{M}=2\) impedances only (\(\bar{M}\leq M\)) \\ Symbol mapping & direct-mapping (\(M\)-to-\(M\)) & reflection coefficient projection (\(M\)-to-\(\bar{M}\)) \\ \hline
**(2) Coding** & [3; 10; 32] & \\ \hline Multiple access & OMA using TDMA & NOMA using sparse code \\ Duty cycle & limited to \(D\leq\frac{1}{N}\) & extended to \(D\leq\frac{K_{1}}{K}\) where \(K\leq N\), \(K_{1}\geq 2\) \\ Codeword & orthogonal (or diagonal) & non-orthogonal and interfering codes \\ \hline
**(3) Detection** & [3; 11; 25] & \\ \hline Diversity combining & \(N\) parallel MRC blocks & integrated MPA with \(\bar{K}\) FNs and \(N\) VNs \\ ML detection & hypothesis test in 2 dimension & projection \& expansion in \(K_{1}\) dimension \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of AmBC systems evaluated in numerical simulations. ambient sources as well as \(N\) multiple RF tags transmitting data to the nearby reader whose locations are random and uncoordinated. For example, we consider the deployment scenario as shown in Figure 9a, but our model can be adapted to general IoT networks as well by simple modification of network/channel-related parameters (e.g., the number of tags \(N\), the tag-reader distance \(d_{\text{T}_{n}\text{R}}\)). When the reader such as a mobile user requests data to these RF tags within the reader's communication range \(R_{\text{R}}=40\) m, the \(N=10\) tags uniformly distributed inside the range can upload \(M\)-ary data based on the proposed sparse codes over \(U=10\) OFDM carriers. Then, the coding parameters \(K_{1}\) and \(K\) are set to satisfy the energy-causality condition for the AmBC systems and used for optimal design of the constellation mapping function and the factor graph. In the MSC-AmBC, codewords are generated by \(\tilde{M}\leq M\) load impedances with low number of projections in \(K_{1}\geq 2\) dimension, and then detected at the reader by the iterative projection and expansion. On the other hand, the TD-AmBC encodes codewords using \(M\)-ary PSK modulator [3] with \(\tilde{M}=M\) impedances modulating data in 2-dimensional signal space represented by the real and imaginary axes of the reflection coefficients and detected at the reader by the MRC [3; 11; 25] of pilot signals.