Dynamic Spectrum Access Decisions. George F. Elmasry

enabled or disabled based on network monitoring and management decisions.

6.5 Power Control, Orthogonality, and 5G Spectrum Utilization

So far, the models we used in Section 6.2 for spatial modeling and in Section 6.4 for cooperative spectrum sensing are at a relatively abstracted level and have not considered other factors such as power control. One can consider that one of the 5G optimization goals is to maximize data rate for the least power consumption and spectrum energy emission in addition to the maximization of throughput in terms of bits per Hertz. The dense deployment of 5G cells allows the end‐user devices to achieve the desired data rate at low energy emission, but power control is still a critical factor in 5G DSM. In 5G, the policy given to a single end‐user device regarding power control has to be dependent on the policies given to other end users. The DSM technique would have to consider an equilibrium (e.g., a gamming theory based equilibrium) while using constraints in order to approach optimality of spectrum assignment at any given point in time.

      One important tool 5G DSM can use before considering power control is signal orthogonality. Spectrum resources are mutually orthogonal blocks²⁰ that can be cognitively utilized for data transmission to maximize data rate for the least power consumption and spectrum energy emission. Orthogonality is a critical tool in reducing SI.

      With power control, Equations (6.3) and (6.4) are no longer enough to drive a model for SIR. Here, SIR encountered by a pair of transmitter and receiver nodes, k, has to consider the resource block n this pair is using. SIR can be expressed in the more general formula:

(6.5)

      In Equation (6.5), notice the following:

       pk, n is the transmit power of the kth transmit/receive pair over the resource block n.

       αk, n, φk, n, and ωk, j, n are positive parameters that depend on the desired systems parameters and propagation model.

       The summation in the denominator is to consider orthogonal signal impact where ωk, j, n depends on the impact of the other users' channels on the resource block n.

       αk, n represents the impact of the kth pair on the signal dimension of the nth block, φk, n.

      Notice that for the special case of perfect orthogonality (where a signal in one dimension has no interference impact on signals in other dimensions), the summation in the denominator becomes zero and φ_{k, n} becomes zero except for the kth dimension, making Equation (6.5) render a simple signal to noise ratio. The 5G DSM model used here considers imperfect channel orthogonality.²¹

      A comprehensive 5G DSM has to face many other challenges, including the following:

      1 Power control has to lead to energy emission optimization in different scenarios, including when spectrum assignment decisions are made through a centralized arbitrator (i.e., the macrocell acting as main fusion center, as in Section 6.4.1) and when spectrum assignment decisions are made autonomously by cell access points, as in Section 6.4.2.

      2 When spectrum assignment decisions are made by a centralized arbitrator, the 5G DSM technique should optimize energy emission globally. A metric for global energy efficiency, EEG, can be used to gauge the efficiency of the decisions reached.

      3 The optimization techniques used can be heuristic and may not render the best optimum way all the time. The DSM technique has to consider the tradeoff between accuracy, computational power, and speed of making decisions using heuristic algorithms. Techniques such as fractional programming and heuristic attempts to create sequential convex optimization in large‐scale dense deployments can become challenging.22

      4 When spectrum assignment decisions are made autonomously by a cell access point, the end‐user device can act in a noncooperative manner (consider the case in Figure 6.14). The end‐user device can be aiming to maximize its own energy efficiency and obtain a certain rate of transmission at the lowest power consumption regardless of the impact of its own arbitration decision on the global optimization of energy emission.

      5 Resource blocks are employed for transmit/receive pairs dynamically and are continually assigned and freed, meaning the optimization problem is always trying to reach equilibrium.

      6 There is a tradeoff between global performance in the centralized case and fairness. In an equilibrium problem settings, fairness has to be less subjective and be about not starving one end user of spectrum resources on the expense of another end user.

      Now let us consider a wireless network with K transmit/receive pairs and N available resource blocks where SIR can be represented by Equation (6.5). Let us assume that for any given user K, energy efficiency can be measured in bit/Joule or the ratio of the achieved transmission rate (from the obtained resource block) to the dissipated power by the device. This device energy efficiency can be expressed as:

(6.6)

      Equation (6.6) can be synthesized as follows:

       pc. k is the power dissipated by the transmitter for the kth transmit/receive pair.

       PK is the power allocation vector over the utilized N resource blocks, which is one of many possible vectors that can be allocated as denoted by in the equation:(6.7)

       The end‐user device has local power constraints , which is the maximum power the device can dissipate. Thus:(6.8)

       In order to create fairness as explained above, we must assure that the end‐user device will have a minimum transmission rate. However, this minimum transmission rate can be illusive if we want to also limit the minimum number of spectrum resources blocks we can assign to an end user. This will require creating a metric that measures the maximum rate that can be achieved for the minimum number of spectrum resource blocks. The term SIRk, nrepresents the maximum SIR we can expect when interference and noise are minimal.

       The end‐user device can be assigned a target data transmission rate in order to achieve fairness. We have to consider that target data rate in terms of SIRk, n. This means the nominator in Equation (6.6) has some boundary data rate. The data rate the end‐user device can achieve, θk, is bounded as:(6.9)

      The goal of the DSM technique is to allocate to each end user a power vector as in Equation (6.7), where the power dissemination of the end‐user device is bounded by Equation (6.8) and the data rate transmission is bounded by Equation (6.9). Globally, the DSM technique generates a feasible²³ set of power for all the transmitting nodes and all the resource blocks. The available combination of the global sets can be expressed as:

(6.10)

The DSM technique generates the feasible set from Equation (6.10), which