Читать книгу Dynamic Spectrum Access Decisions - George F. Elmasry - Страница 102

Let us define the metric “connectivity” as the probability that a pair of nodes in a network will be able to exchange information at a specified rate R through a single over‐the‐air hop. There is a threshold β for SIR that can be used in a simple manner to express connectivity where connectivity can be assumed to occur if Pr[SIR > β]. That is, if the estimated SIR is less than β, the node pair would decide that a link is not possible.⁹ The desired rate R can be expressed in bits per second (bps) and can be estimated from β using the Shannon's equation as follows:

(6.2)

In Equation (6.2), Γ ≥ 1, which represents the collective interference impact on data rate.¹⁰ The node pair would calculate SIR from Equation (6.1) and calculate β from Equation (6.2) and decide if single over‐the‐air hop connectivity is possible or not.¹¹

In 5G, connectivity has many use cases. Consider the following use cases:

1 If there are no other cells using the same frequency in the area (5G can be considered to be operating much 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.