like Figure 6.4) and there is a single active end user, the coverage area for a given rate is decided by the SIR estimation in Equation (6.1) and the threshold β in Equation (6.2) is calculated in a straightforward manner. If SIR > β, the end‐user device has to simply refrain from transmitting when receiving to avoid SI in order to maintain the desired data rate.2 If a source and destination pair have to communicate through one or more relay nodes, a path must be found where all of the over‐the‐air hops satisfy Equations (6.1) and (6.2). When there is a single flow, as shown in Figure 6.5, this estimation is also straightforward provided that interleaving of transmit and receive time is done accurately to prevent SI between all node pairs in the path.
3 When there are more than one flow, all flows have only one over‐the‐air hop, and there is one flow per cell, connectivity calculation will use the summation in Equation (6.1) to consider all transmitting and receiving node pairs. This case is illustrated in Figure 6.6. Here, accurate directionality, power control, and narrowing the beam as much as possible can reduce the effect of SI.
4 The general case when there is more than one flow and flows use relay nodes. With this case, there are different ways to describe network connectivity based on the single over‐the‐air hop connectivity. Reaching full network connectivity means that all communicating pairs and all single over‐the‐air hops meet the conditions in Equations (6.1) and (6.2).12 With this case, interleaving transmit and receive time per each node is not sufficient to avoid interference. Spatial separation becomes more complex and DSM is needed to ensure connectivity. This case is covered in more detail in Section 6.2.3.
Figure 6.5 Single flow in a cell area of coverage.
Figure 6.6 Multi‐flow, each with a single hop to a different cell.
6.2.3 General Case Connectivity and Coverage
Connectivity and coverage for the 5G general case are multifaceted. This section covers two important aspects of the general case: transmission capacity and cell overlay. There are more aspects of connectivity and coverage and how they relate to DSM in 5G but these two aspects should give the reader the important basis for 5G DSM.
6.2.3.1 Transmission Capacity
The main goal of DSM is to increase the network throughput or transmission capacity in a given area. Given that in 5G we have mobile users and cells that can also be mobile, we can conceptualize a 5G network as an ad hoc wireless network while putting aside the backhaul wired links. The goal here is to create a spatial metric in which throughput is measured as a function of both rate of transmission and the distance between the transmitting and receiving nodes. We not only put aside wired backhaul links, we also put aside the effect of implementation specific techniques such as physical layer algorithms and channel access protocol. The goal here is to create a spatial metric that is generic enough and points to some fundamental properties of the 5G network. The analysis below has the sole goal of pointing to spatial metrics as the problem domain can get complicated if we want to create a comprehensive model.
Let us consider the model in Figure 6.7, where we have transmitting and receiving pairs with the direction of transmission selected randomly. The transmitter and receiver locations can also be selected randomly within a given range such that the distance between a transmitter and the receiver, r, is bounded. If we do not consider interference due to background noise, we can create a formula that points to the most critical metric for the DSM technique to consider. If the DSM technique has a set target for SIR threshold as β, it can assume a Rayleigh fading model. With this model, the probability that SIR exceeds the threshold β is:
(6.3)
where λ is the density of transmitters13 and C(α) is a function of α used to simplify the formula by consolidating the Rayleigh α parameter impact.
Figure 6.7 Transmission capacity general model. Triangles represent idle nodes, black squares represent transmitting nodes, and white squares represent receiving nodes.
For SIR to be less than β, a link closure must have failed. Thus, the transmission capacity in a given area can be related to an outage constraint ε, where the successful transmission in the given area (unit area) can be expressed as:
(6.4)
Equation (6.4), with its simplification approach of a complex problem domain, can point to the following critical aspects:
1 In a large ad hoc network, transmission capacity decreases as a function of r2. This can lead to the concept of sphere packing where each successful transmission utilizes a ground area that depends on the distance between the transmitter and the receiver.
2 The selected SIR threshold is critical. This is not a predetermined threshold. Cognitive techniques search for the SIR threshold that maximizes the area's spectral efficiency.
3 Transmit and receive node pairs can't be chosen in this model. Any node can be a transmitter or a receiver at any given time.
4 Although beam forming, spread spectrum, power control, and other DSA techniques are not included in this simple model, their impact can be reflected in the reduction of SIR, which leads to increasing spectral efficiency in Equations (6.3) and (6.4).
5 Other generalizations such as multihop transmission can be added to this model. Note that some cognitive techniques
