6.4 Traditional cellular frequency spatial separation planning.
With 5G and the dense deployment of different size cells, a received signal is impacted by the distance between many transmit and receive pairs using the same frequency. 5G includes overlay of different technologies and different access points, which have different areas of coverage that can overlap. Cellular 5G is heterogeneous in many aspects, including the following:
1 The deployment of different cell types, as shown in Table 6.1. Each cell type can have a different area of coverage and these areas can intersect and be overlaid on top of each other.
2 The mixed use of FD links, with directionalities to increase spectrum reuse, with LTE links that separate the uplink from the downlink channels.
3 The opportunistic use of available spectrum mixed with the use of provisioned spectrum.
4 The mix of unplanned deployment of 5G cells, which may or may not have fiber connectivity to the core network, with LTE fixed infrastructure.
5 The ability to operate in a very wide range of frequency bands spanning from below 6 GHz to 102.2 GHz.
In essence, cellular 5G provides high capacity access through randomly located nodes (end users and cells), irregular infrastructure, and dynamic spatial configurations. The cellular 5G paradigm is a major shift from previous cellular technologies that require the use of different spatial models.
The impact of the distance between the transmitter and the receiver on signal power has been studied with different propagation models. Wireless systems have long been designed based on link‐budget analysis, fading margins, and the ability to tradeoff range for transmission rate. The 5G paradigm requires transmit and receive node pairs to continually consider the timely use of a frequency in light of spatial separation to avoid excessive interference. In the multidimensional spectrum sensing model presented in the previous chapters, space becomes the most challenging dimension to model with cellular 5G. While time and frequency separation is easier to model, space modeling encounters the leakage of undesired signals and the impact of co‐site interference in addition to the continual change in the transmitting and the receiving nodes locations. 5G has limited practical options to reduce interference keeping in mind that reducing signal power would reduce the signal to interference ratio (SIR)6 while increasing signal power will reduce the chance of spectrum reusability.
6.2.1 Spatial Modeling and SIR
Spatial modeling in 5G can use a set of metrics that can affect SIR. SIR becomes an instantaneous ratio of desired energy to all the additives of undesired interferences and noise. Thus SIR can be considered a random variable that depends on a set of factors that include the following:
1 The distance between the transmitting node and the receiving node. Much like traditional signals, this factor can be modeled by a path loss model. All path loss models follow an inverse‐power law with an exponent trend. For example, in a free space model, signal power decrease with distance in a quadratic trend. Other path loss models can use different exponent values to model signal scattering and signal absorption.
2 The number of active transmitters in a given proximity. For a given receiver, and during the time of reception, there are different potential combinations of active transmitters where their signal will appear as interference. The sum of interference power from all the transmitting nodes, taking into consideration their distances from the given receiver, has to be modeled. In a dense deployment of 5G cells, this sum of interference power from other transmitters can exceed the noise power threshold that is selected to ensure reliable connectivity.
3 The ambient noise. SIR will be affected by noise power and this noise will depend on the received signal and the interference power. Notably, if a 5G deployment resorts to lower transmission power, the ambient noise impact on SIR can be the larger factor. On the other hand, if a 5G deployment resorts to a high transmission power, the sum of interference power in step 2 above becomes the larger factor.
4 Other factors. There are many other factors that can affect the SIR calculation such as fading and shadowing, transceiver design (e.g., the use of multiple antenna and interference cancelation techniques), and adaptive power control.
A simple representation of SIR at a typical receiving node can be expressed as:
(6.1)
where o represents the origin in the spatial model assuming the receiving node is at the origin of the spatial plan, hio is the fading coefficient of the channel at the receiving node for the signal transmitted from node i, ρi is the transmit power of transmitter i, No is the noise power, Φ is the set of all interfering nodes,7 and Xi expresses the distance between the ith interfering node and o.
Notice that Equation (6.1) performs the following:
1 It puts the receiving node at the origin of the spatial model o making the calculation with respect to o.
2 It creates a probabilistic spatial model where transmitting nodes can be randomly positioned with respect to the origin.
3 It consolidates path loss calculation of the subset of transmitting nodes presumed to cause interference with the receiving node at the origin.
Equation (6.1) can be used in a spatial model to calculate SIR, which can be used in a 5G dense deployment to calculate connectivity and coverage when assigning spectrum resources. In addition, SIR calculation can be used to estimate the capacity and throughput of a given deployment area. This calculation can further lead to collecting metrics that can measure the reliability of the 5G networks.8
6.2.2 SIR and Connectivity
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
