## 4 Scenario and Parameterization
### Parameterized TDM Pattern  
In this work, for a tractable delay estimation, we considered the following fixed parameterized TDM pattern. The pattern was repeated every \(2T\) ms and consisted of two equal macro-phases. During the first macro-phase of length \(T\) ms, i.e., in time intervals \([2 nT,(2n+1)T)\), \(n\in\mathbb{N}\), all the network nodes in odd tiers (Tiers 1, 3, etc.) transmit, while all the network nodes in even tiers (Tiers 2, 4, etc.) receive. During the second half of the pattern, i.e., in time intervals \([(2n+1)T,2(n+1)T)\), \(n\in\mathbb{N}\), the opposite happens: all the network nodes in odd tiers receive, while all the network nodes in even tiers transmit. Each macro-phase is divided into the backhaul and access micro-phases. For the sake of synchronization, the backhaul micro-phase comes first, followed by the access micro-phase. While the macro-phases are common for the whole network, the ratio between micro  
Figure 5: Studied topologies. Figure 6: Deployment example of Topology # 2: red dots represent IAB-donors; green dots represent IAB-nodes. phases, i.e., between backhaul and access, can be set individually for each pair of connected sectors or network tiers. It is convenient to specify the backhaul/access micro-phase durations by an \(N\times N\) matrix, say \(\mathbf{D}=(D_{i,j})_{i,j=1,\ldots,N}\), where entry \(D_{i,j}\in[0,1]\) indicates the portion of the macro-phase the backhaul link from node \(i\) to node \(j\) is activated. To illustrate the above notation, let us go back to Figure 3 and consider an example. Here, Sectors 1, 2, and 4 of Node 1 do not support backhaul links, and Node 1 belongs to Tier 1 (odd); therefore, the TDM patterns for these sectors will be:  
1. \(0\leq t<T\): transmit access;
2. \(T\leq t<2T\): receive access. Exactly the same pattern will be followed by Sectors 1 and 3 of Node 3, since it also belongs to an odd tier (Tier 3) and these sectors have no backhaul links. Sector (2,3) has no backhaul link, but the node belongs to an even tier (Tier 2); hence, it follows the symmetrical pattern:  
1. \(0\leq t<T\): receive access;
2. \(T\leq t<2T\): transmit access. Now, Sectors (1,3) and (2,1) are linked to each other (\(M_{1,2}=3\) and \(M_{2,1}=1\)). To activate the link between them in either direction, the TDM pattern of these sectors must contain a non-zero backhaul micro-phase. To specify the lengths of these micro-phases, we used parameters \(D_{1,2}\) and \(D_{2,1}\). Transmission from Node 1 to Node 2 is possible only when Node 1 is transmitting and Node 2 is receiving, i.e., during the first macro-phase of the pattern. This macro-phase lasts \(T\) ms and is divided into the backhaul and access micro-phases by the parameter \(D_{1,2}\): the backhaul lasts \(D_{1,2}T\) ms and the access \((1-D_{1,2})T\) ms. Parameter \(D_{2,1}\) characterizes the transmission from Node 2 to Node 1 and, hence, specifies the subdivision of the second macro-phase into a backhaul micro-phase of length \(D_{2,1}T\) and an access micro-phase of length \((1-D_{2,1})T\). Thus, Sectors (1,3) and (2,1) follow symmetrical patterns of the form:  
1. \(0\leq t<D_{1,2}T\): (1,3) transmits backhaul, (2,1) receives backhaul;
2. \(D_{1,2}T\leq t<T\): (1,3) transmits access, (2,1) receives access;
3. \(T\leq t<T+D_{2,1}T\): (1,3) receives backhaul, (2,1) transmits backhaul;
4. \(T+D_{2,1}T\leq t<2T\): (1,3) receive access, (2,1) transmits access. Table 2 gives the TDM patterns for sectors \((i,M_{i,j})\) and \((j,M_{j,j})\) for any \(i\) and \(j\) such that \(M_{i,j}>0\) in the general case. The application of non-synchronized TDM patterns in the network of Figure 3 is illustrated in Figure 7. Here, \(T=6\) transmission time intervals (TTIs), and the durations of the backhaul micro-phase in different backhaul-supporting sectors were set \(\frac{5}{3}T\), \(\frac{1}{2}T\) and \(\frac{1}{3}T\). Non-synchronized micro-phases in linked sectors lead to channel downtime and the waste of resources.