# Multi-Dimensional Sparse-Coded Ambient Backscatter Communication for Massive IoT Networks
## 2 System Model
### Ambient Source Model  
We consider the multi-dimensional sparse-coded ambient backscatter communication (MSC-AmBC) network embedded with \(U\) multiple ambient sources emitting RF signals which can be utilized for AmBC, \(N\) concurrent RF tags employing sparse codes to represent \(M\)-ary data in multi-dimensional signal space and a single reader separated from the sources as depicted in Figure 1. Typical example of the RF sources includes TV stations [1; 2] in digital video broadcasting (DVB) network, Wi-Fi AP [3; 12] in wireless local area network (WLAN), small-cell base stations in beyond 4G/5G [28; 29; 30], all of which are not dedicated to the reader. Among various modulations, the most common scheme employed here is an orthogonal frequency division multiplexing (OFDM). In an OFDM carrier, there are \(L\) multiple subcarriers with low power (e.g., +20 dBm in Wi-Fi) in frequency domain for high-rate data transmissions against frequency-selective channel. Specifically, \(L\) subcarriers in ambient source signals can be classified into 3 groups of subcarriers: data, pilot, guard (null). At ambient source \(u=1,\cdots,U\) for time slot (OFDM symbol period) \(k=1,\cdots,K\), these subcarriers can be summarized as  
* **Data Subcarriers:** There are \(L_{\text{D}}\) data subcarriers with \(M_{\text{D}}\)-ary modulation. Symbols in data subcarriers are denoted by \(\rho_{\text{D}}(l,u,k)\in\mathcal{A}_{\text{D}}\), \(l\in\Phi_{\text{D}}\) where \(\mathcal{A}_{\text{D}}\) is the alphabet set of data subcarriers with cardinality \(|\mathcal{A}_{\text{D}}|=M_{\text{D}}\) and \(\Phi_{\text{D}}\) the index set of data subcarriers with cardinality \(|\Phi_{\text{D}}|=L_{\text{D}}\). These subcarriers are used to transmit data intended for legacy receivers but unknown to the reader which has to decode backscattered signals from multiple tags. * **Pilot Subcarriers:** There are \(L_{\text{PI}}\) pilot subcarriers with \(M_{\text{PI}}\)-ary modulation. Similar to the above, symbols are denoted by \(\rho_{\text{PI}}(l,u,k)\in\mathcal{A}_{\text{PI}}\), \(l\in\Phi_{\text{PI}}\) where \(\mathcal{A}_{\text{PI}}\) is the alphabet set of pilot subcarriers with cardinality \(|\mathcal{A}_{\text{PI}}|=M_{\text{PI}}\) and \(\Phi_{\text{PI}}\) the index set of pilot subcarriers (e.g., 12, 26, 40, 54 in 802.11g Wi-Fi) with cardinality \(|\Phi_{\text{PI}}|=L_{\text{PI}}\). The pilot subcarriers are required for channel estimation in the legacy OFDM system and generated by known sequences. When the preamble of OFDM frame is received by the reader, the symbols in these subcarriers can be efficiently acquired at the reader. Hence, the pilot subcarriers can act as spreading sequences [11; 12; 25] enabling reliable AmBC for RF tags. * **Guard Subcarriers:** There are \(L_{\text{G}}\) guard subcarriers with index \(l\in\Phi_{\text{G}}\) where \(\Phi_{\text{G}}\) is the index set of guard subcarriers. These subcarriers contain no power to prevent inter-carrier interference from adjacent OFDM carriers and not related to the AmBC systems. Figure 1: System architecture of MSC-AmBC over multiple OFDM carriers. Accordingly, the frequency-domain ambient source signals are composed of the active \(L_{\text{A}}=L_{\text{D}}+L_{\text{PI}}\) subcarriers and the inactive (null) \(L_{\text{G}}\) subcarriers as depicted in Figure 2. Thus, the total \(L=L_{\text{A}}+L_{\text{G}}\) subcarriers whose indices belong to \(\Phi=\Phi_{\text{D}}\cup\Phi_{\text{PI}}\cup\Phi_{\text{G}}\) are generated in each source \(u\) during OFDM symbol period \(T_{s}\). Since there are \(U\) OFDM carriers actively generated from sources and \(N\) OFDM carriers passively reflected from RF tags, there exist \(U+N\geq 2\) multiple OFDM carriers, further complicating detection of AmBC signals (i.e., \(U+N=2\) is common in the conventional AmBC system design [1; 2; 3; 11; 12; 25; 31; 32]).