Читать книгу Dynamic Spectrum Access Decisions - George F. Elmasry - Страница 104

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 can search for the best multihop path utilizing the r2 impact and SIR threshold shown in this model.

Equation (6.4) makes it possible to consider the transmission capacity problem starting from a simple model.