3.1.1 Background and Motivation of a Self‐Sustaining Wireless NAN

In a neighborhood powered by the smart grid, each household or apartment (we will use only household hereafter since the DAPs are not affected by the types of customers) is equipped with a smart meter. Besides residential customers, commercial and industrial customers are also equipped with smart meters in their buildings and parking lots with electric vehicle charging ports. Each smart meter collects facility status and customer‐side power usage. Smart meters are connected to the service provider through the NAN and WAN to upload customer information to the service provider. The service provider sends real time pricing and tariff information to all the smart meters through downlinks.

A NAN consists of multiple DAPs. Each DAP collects data from a group of nearby smart meters. Unlike a HAN, which is deployed in a protected household, a NAN is most likely to be deployed in an open public area; it must be low‐profile and flexible so it can be easily deployed, moved, or replaced. Unlike a WAN, which is powered by the grid directly and has a wired connection to satisfy its Gbps‐level data rate, a wireless‐based NAN has a much lower data transmission rate. Fortunately, a NAN does not require a Gbps‐level data rate. In practice, a smart meter generates about 12 KBytes of data during one sampling period [34]. In that case, short‐range wireless technology such as Wi‐Fi would provide sufficient performance for local transmission within a NAN [58]. Moreover, operating a wireless‐based NAN does not require too much power, which makes it possible to apply renewable energy (e.g. solar power) to the NAN design.

However, Wi‐Fi is not a good solution to longer distances (e.g. uplink/downlink transmission of NAN gateways to/from the concentrator). A solution is to use cellular communication technologies, for instance IEEE 802.16 (WiMAX) [59], for NAN gateways. Note that the term gateway is used interchangeably with NAN gateway in the rest of the chapter. Ideally, WiMAX provides a data rate up to 70 Mbps and distance up to 48 kilometers [60]. Although those two cannot be achieved at the same time, a high data rate can be achieved when the distance is relatively short in a neighborhood. WiMAX also has an advantage over other types of longer distance wireless transmission (e.g. LTE) in that it can be operated in an unlicensed spectrum under FCC rules [61].

Since a larger number of hops in a mesh network results in a longer delay [62], some gateways need to be deployed in the NAN. In addition to reducing end‐to‐end delay, multiple gateways would also enhance the reliability of the NAN [63]. However, a larger number of gateways does not necessarily produce better transmission performance. It is important to find the optimal number of gateways in a NAN. In this design, we will focus on the scenario with a single concentrator.

3.1.2 Structure of the Proposed NAN

The proposed self‐sustaining wireless NAN design is based on an IEEE 802.11s-enabled (or Wi-Fi based) [64] wireless mesh structure. An overview of the NAN design is shown in Figure 3.1. The NAN consists of a concentrator and a number of DAPs. The concentrator is deployed close to the neighborhood. It is connected to the wired backhaul network for communicating with the service provider. DAPs are deployed to cover the entire neighborhood. Each of them collects data from several surrounding smart meters and uploads the data to the concentrator. Each DAP also broadcasts controlling information from the service provider to those smart meters.

IEEE 802.15.4 (ZigBee) has been widely adopted for HANs and thus is assumed to be the technology used for communications within a HAN and between a HAN and a DAP [64]. Unlike the single‐hop low data rate transmissions between a HAN and a DAP, local NAN transmissions among DAPs introduce multihop wireless mesh networking. Therefore it requires a higher data rate for the transmissions. IEEE 802.11s (Wi‐Fi‐based wireless mesh network) is a good candidate, since it meets these criteria. Among all the DAPs, some of them are chosen as the gateway DAPs which communicate with the concentrator directly. Although Wi‐Fi performs well in local NAN transmission, its transmission range is limited; therefore it can hardly support uplink and downlink transmission between gateway DAPs and the concentrator at longer distances (i.e. hundreds of meters). As a solution for gateway DAPs, we adopt IEEE 802.16 (WiMAX) as the technology for transmission. Using WiMAX has an extra benefit compared with similar technologies (e.g. UMTS or LTE). WiMAX can be deployed using an unlicensed band (e.g. ) in order to lower the service cost by avoiding license fees for band access. However, the use of unlicensed bandwidth must follow certain restrictions imposed by the FCC [61].

Normal DAPs are deployed in the neighborhood to cover all customers. The number and the geographical positions of gateway DAPs must be carefully chosen so that the data from all the customers can reach the concentrator in time. Traditionally, a network may only have one or multiple gateways that are located closer to the destination compared with other units within this network. However, multiple gateways need to be deployed sparsely in a NAN because of its wide‐ranging latency requirement (3 ms to 5 min) [65, 66]. If some metering data has too many hops to reach a gateway, it may not get delivered within the latency requirement.

To achieve self‐sustainability, the DAPs are powered by renewable energy (e.g. solar power). Compared with the design powered by a power line, using renewable energy will significantly reduce the construction cost, since the location for deploying a DAP does not need physical access to a power outlet. The flexibility and lower cost also ease the burden of maintenance and system upgrades (e.g. replacement or relocation of the DAPs) in the future. Moreover, a system that must be plugged into an outlet will be useless during emergency situations such as an outage. However, during such blackouts it is critical for the service provider to get power line status or to send out control messages. Therefore, being independent of the traditional power supply is an advantage of the proposed wireless NAN design.

3.2.1 Charging Rate Estimate

The charging rate estimate is modeled for a solar panel that powers a DAP. For simplicity, we assume that the maximum charging rate occurs at noon (assuming 12:00 p.m.) and the minimum charging rate occurs at sunrise and sunset. Moreover, let the charging rate be symmetric during the daytime. Then the charging rate at time with perfect weather conditions is estimated as follows:

(3.1)

where , is the parameter that determines the (e.g. noon/sunrise) charging ratio, is the weight factor depending on number of the solar panels and weather conditions, and are sunrise time and sunset time respectively. In other words, is a value determined by the nature of the solar panel, and is determined by the size of solar panel.

For example, as stated in [67], the charging ratio with sunny weather conditions is about 2.94. Even with cloudy weather conditions, the solar panel can still generate electricity with a charging ratio of about 2.33. With these facts, we find and for sunny and cloudy weather conditions respectively. Although a solar panel still functions with imperfect weather conditions, it generates electricity at a significantly lower rate. The ratio of the maximum charging rate during sunny weather to that of cloudy weather is about 6.71. Equivalently speaking, we have . If a unit solar panel has a maximum charging rate of 1 W during sunny weather, then its and . The charging characteristics during perfect weather conditions of such a solar panel unit are shown in Figure 3.2. Without loss of generality, cloudy weather is applied to illustrate all bad weather, such as rainy or foggy conditions.

Although the performance of a solar panel varies in different seasons, we assume the size needed is determined based on the worst season (normally winter). In the rest of the paper, for simplicity we assume the sunny weather and cloudy weather conditions are those of typical days in winter.

3.2.2 Battery‐Related Issues

The first issue for a battery is the charging cycle. The battery has to be replaced if its state of health (SoH) falls below of rated capacity [68]. The is updated after one charge; for simplicity, we adopt the linear estimation as:

(3.2)

where is the maximum battery life cycle, is the rated capacity, and is the effective capacity highly effected by discharging current for discharging time (typically 20 hours), where

(3.3)

However, the discharging current for a DAP is relatively small (), and thus . In the following discussion, the effective capacity is thus omitted. To make the illustration clearer, let the deterioration of health () be the status of the battery to monitor. And thus accordingly. We rewrite Eq. (3.2) as:

(3.4)

For simplicity, we assume that the maximum battery life cycles depends solely on the depth of discharge (DoD); for example, when , .

(3.5)

We model the maximum cycles under different with several linear segments based on data given in Table 3.1 [69]. The estimates are calculated by Eq. (3.5). Figure 3.3 also illustrates the estimates of maximum cycles with different depths of discharge.

Depth of discharge ()	Maximum cycles
100	300
80	500
50	1200
25	2000
10	4000

3.2.3 Path Loss Model

The uplink transmission from a gateway DAP to the concentrator is usually further than a close‐in reference distance (e.g. 100 m), and it is much further than a single‐hop local transmission; therefore we need to apply path loss to the transmission model. Path loss is not considered in Wi‐Fi transmission within the NAN. Wi‐Fi transmission loss has been considered as the receiving data rate being significantly lower than theoretical limit of the physical layer data rate. There are two well‐known path loss models used to estimate the WiMAX path loss in smart grid communication: one is the modified Hata model (also known as the COST 231 model) and the other one is the Erceg model [70].

The modified Hata model is applicable from 1500 MHz to 2000 MHz and with a frequency correction factor can be extended to higher frequencies. The path loss is calculated as

(3.6)

where is the path distance in kilometers, is the frequency in megahertz, is the base station (concentrator) antenna height, is the subscriber station (DAP) antenna height, and is calculated as:

(3.7)

For urban environments,  = 3 dB and

(3.8)

For suburban environments,  = 0 dB, and

(3.9)

The Erceg model is considered applicable from 1800 MHz to 2700 MHz; it also adopts a correction function for higher frequency. The path loss is calculated as:

(3.10)

In addition to the parameters used in the modified Hata model, here  m, and is the wavelength in meters. The correction function [71] for higher frequency is

(3.11)

where  MHz and in most settings. The Erceg model has three sets of settings which apply to three terrain types. Type A is hilly with moderate to heavy tree density, type B is hilly with light tree density or flat and moderate to heavy tree density, and type C is flat with light tree density. The detailed settings are shown in Table 3.2.

Suppose that the WiMAX operates at the 5.8 GHz unlicensed band, the path distance  = 2 km, the concentrator antenna height  = 10 m, and the DAP antenna height  = 2 m. The modified Hata model in a suburban environment gives . As a comparison, the Erceg model [71] in hilly terrain with light tree density or flat terrain with moderate to heavy tree density gives 139.67 dB. The two models give close results; therefore, we adopt the modified Hata model for simplicity. Applying the maximum transmission power  dBm allowed by the FCC, the receiving power is  dBm respectively, which is higher than the receiving sensitivity (widely accepted as −120 dBm). Apparently, operating at a lower licensed band will lead to lower path loss.

3.3.1 The Cost Minimization Problem

Generally speaking, the ultimate goal in the NAN design is to minimize the total cost for the NAN to operate for a certain number of years, for example, years. The total cost of a NAN consists of three parts: deployment cost, operational cost, and maintenance cost. Deployment cost includes the cost of all the hardware, including DAPs, gateway DAPs, batteries, solar panels etc. Operation cost includes power usage (which is zero for renewable energy), the data subscription fee if a licensed band is used, etc. And maintenance cost includes the replacement of any malfunctioning equipment, plus labor costs and any monetary loss due to missing data.

In reality, the NAN is supposed to handle a small amount of data; thus it is safe to assume that a self‐sustaining network without maintenance is more cost efficient. By adopting pure renewable energy and unlicensed bands, the operation cost is excluded as well. Therefore, it is reasonable to assume that the total cost for the NAN depends on the deployment cost only. In our NAN design, the equivalent problem is to find the optimal combination of battery size and solar panel size for each DAP so that the minimum total cost could be achieved. Let be the price of a unit size battery (e.g. 1 Wh), and be the price of a unit size solar panel. For the deployment, the objective is to find

(3.12)

where is the battery size, is the solar panel size for DAP , and is the set of all DAPs. For a DAP to sustain the system for years, its battery must last days before reaching the end of its state of health, that is, . Thus the battery is not supposed to be charged every day according to previous discussions. The battery should be charged only when its remaining energy falls below a threshold . This threshold is set based on a critical situation, e.g. continuous cloudy days, as follows:

(3.13)

where is the charging rate for DAP in cloudy weather and is the power usage at time . Let the original battery capacity of DAP be . For practical purposes, we also set the charging threshold to be no less than , such that

(3.14)

Note that will trigger the charging signal; however, the actual charging may not happen immediately. For example, the threshold may be reached during night time. Assuming that is reached at , then at sunrise time , the remaining battery capacity will be . In this case, if the next day is a sunny day, the battery should be fully charged at sunset on that day. If the battery cannot be fully charged on a sunny day, it will not be fully charged under any circumstances. Because once , the indicator of charge is off, and the next charge cycle occurs when . However, the battery will not fully charged again, and the DAP consumes power for the whole day ().

The sunny day charging constraint is set as follows:

(3.15)

where is the charging rate in a sunny day at time . Note that the daytime power consumption is merged with the previous nighttime power consumption and is expressed as the whole day power consumption. To make the illustration clearer, we also show in Eq. (3.16) that on a sunny day at sunrise time , the charging rate is already above the corresponding power usage, such that

(3.16)

A larger solar panel is able to charge the battery faster; however, waste in resources needs to be avoided. Thus, let the upper bound be set such that the DAP can be self‐sustaining if every day is cloudy throughout years. Thus the constraint for the solar panel size is shown in Eq. (3.17).

(3.17)

Moreover, the battery must survive the designed life cycle, such that

(3.18)

Constraint Eq. (3.18) is further relaxed for simplicity and with the practical purpose of finally solving the optimization problem. We define as an estimate of the pseudo‐shortest charging period for DAP . It is estimated based on a fully charged DAP that operates through continuously cloudy days before it reaches the threshold. Thus is estimated as follows:

(3.19)

where returns the larger element of the two. The denominator is the remaining energy before a charging signal is triggered. The numerator is the DAP power consumption in a whole day, which consists of two parts. 1) is the nighttime power consumption, and 2) is the daytime power consumption. Obviously, if , the DAP is powered by its solar panel and does not consume battery energy. Note that is not the shortest delay between two charges because a DAP with a partially charged battery that operates through continuous cloudy days may cause a shorter delay between two charges. However, if only extreme cases are considered, the design will end up with unnecessarily large battery and solar panel. The parameter is validated to be practical in the case study.

Let be an estimated maximum charging cycle based on a deep (e.g. 500 when ). In order to survive the designed life cycle, instead of using constraint Eq. (3.18), we apply the following constraint:

(3.20)

The DAP needs to record several types of data in two consecutive days (e.g. days and ) for further evaluation. First, it needs to record a time stamp when for the first time and also record on each day, (e.g. for day ). The DAP also needs to record a daily charging cycle indicator (e.g. for day ). If , then , where is an XOR function. Note that the battery will be charged at most once per day. Another indicator to be recorded is . Based on and , is calculated as follows:

(3.21)

where is determined by according to Eq. (3.5).

DAPs are independent of each other, as they do not share solar panels or batteries. Therefore, the total cost optimization problem can be approached individually for each DAP if the number of normal DAPs and gateway DAPs are determined (which will be discussed later). Therefore, solving the problem shown in Eq. (3.12) is equivalent to solving the problem as follows:

(3.22)

subject to

Constraints (3.19) and (3.20),

(3.23)

(3.24)

(3.25)

(3.26)

Assume each DAP operates at a constant power consumption (i.e. ). After applying the charging rate estimation functions, new constraints Eq. (3.23), Eq. (3.24), Eq. (3.25), and Eq. (3.26) are rewritten from Eq. (3.13), Eq. (3.17), Eq. (3.15), and Eq. (3.16) respectively. With any given , Eq. (3.22) is a linear optimization problem that can be solved efficiently. For normal DAPs, which are basically Wi‐Fi routers, their power consumption is constant (e.g.  mW or  dBm). Therefore, the cost for normal DAPs can be determined so far. However, the power consumption for gateway DAPS ranges from 100 mW to 1 W. The method of deployment and number of gateway DAPs would highly affect the service quality to customers. It is not recommended to arbitrarily assign a power consumption level to a gateway DAP. Therefore, we need to first determine the number of gateway DAPs and then optimize the uplink transmission power consumption for each of them.

3.3.2 Optimal Number of Gateways

In much of the research regarding power control for multiple‐access systems [72–75], the effective transmission rate (or the receiving data rate) for a transmitter (e.g. gateway DAP ) is expressed as follows:

(3.27)

where is the physical layer transmission rate and is the signal‐to‐interference‐plus‐noise (SINR) ratio. The SINR is calculated as follows:

(3.28)

where is the processing gain. In Eq. (3.27), is the efficiency function that calculates the probability of a packet being successfully transmitted. Function is widely adopted as an increasing, continuous, and S‐shaped function with , predetermined. Mathematically, the efficiency function can be as follows:

(3.29)

where is the packet length.

Let be the indicators of gateway DAPs, and be the total number of gateway DAPs. We then discuss the optimal needed for a specific NAN. Since usage, coverage, and customer numbers of the smart grid, the optimal number is one that supports a maximum upload transmission data rate in a NAN that provides for future upgrades. This problem is formulated as follows:

(3.30)

where is the set of positive integers. We assume that each gateway DAP covers the same number of users regardless of its distance to the concentrator. Then the receiving power at the concentrator for each gateway needs to be identical, that is, , so that all smart meters will be treated fairly independent of their distance to the gateway. Since shall be a constant for later discussion, we replace it with a variable for solving Eq. (3.30) in this subsection. Eq. (3.28) is then rewritten as follows:

(3.31)

For simplicity, path gain is represented as follows:

(3.32)

where is the distance between the gateway and the concentrator and is the fading parameter. Thus the receiving power can be written as

(3.33)

Obviously, increases with respect to , . The maximum SINR is achieved when . Note that depends on the furthest gateway, since it has the lowest path gain. Thus the maximum SINR is calculated as follows:

(3.34)

Note that the noise (e.g. −120 dBm) is not negligible compared with (e.g., −110 dBm). With a given , the efficiency function is a function with respect to (note that is a positive integer) such that

(3.35)

The estimated maximum total transmission data rate from all the gateways is calculated as follows:

(3.36)

With that, the objective in Eq. (3.30) can be presented equivalently as follows:

(3.37)

Let , then can be calculated equally as follows:

(3.38)

Now that we know Eq. (3.38) is quasiconcave, it has a unique maximizer [76] which can be found by calculating [76]. To this end, the optimal number of gateways is found as follows:

(3.39)

where .

3.3.3 Geographical Deployment Problem for Gateway DAPs

Intuitively, if the gateway DAPs are deployed close to the concentrator, they would have the best network performance. However, metering data from those customers who are further away from the concentrator will go through more hops before finally reaching the concentrator and thus incur longer delays, which decrease the quality of service provided to them. Therefore, the purpose of the geographical deployment of gateway DAPs is to let all the customers get high‐quality service.

Without loss of generality, the neighborhood is assumed to be a square block with side length . Houses are usually built in a grid topology such that the smart meters are close to uniform distribution. DAPs also need to be deployed as uniformly as possible so that each customer can be fairly served. The fairness also applies to gateway DAPs. Achieving exact fairness for all customers is beyond the scope of this work, and it can hardly be done considering solely the geographical deployment. We then propose a method to approach some geographical fairness. Further fairness can be achieved through the routing scheme in the local multihop transmission.

In an area that covers (e.g. 1 km), gateway DAPs are to be deployed (or chosen from existing DAPs). Each gateway DAP shall cover an area of in order to be fair. Suppose the coverage of a gateway is a disk shape, then the radius of an individual disk is . Let the gateway DAPs be deployed on a set of virtual rings which are centered at the concentrator. The number of rings depends on and . Due to the symmetric nature of the topology, we only need to process a half of it (e.g. the right half). Within , at least gateway DAPs are needed horizontally. That indicates rings. For example, if , respectively. The virtual rings are then evenly placed in the neighborhood with a radius increment of starting from the most inside one, where is the radius of the smallest ring. The smallest radius is also the closest distance from the most outside ring to the edge of the neighborhood. Therefore, , and the radius of ring is . As shown in Figure 3.6, varies according to different . The idea here is to let the gateway DAPs cover the network as evenly as possible.

Once virtual rings are established, gateways can be distributed on the rings. On each ring, the gateways are roughly away from each other; therefore, the maximum number of gateways on a ring is as follows:

One may have realized that not all gateways are guaranteed to be deployed on the virtual rings evenly. Thus we determine the number of gateways on each ring first and then deploy them on each ring. Let be the set of distances from gateways to the concentrator. Each distance reveals the ring that gateway is deployed. We propose two methods to find the set of distances .

In the first method, gateways are deployed one on each ring, starting from the outermost ring. The maximum number of gateways on each ring is determined by . Using and d = 1 km, the deployment is illustrated in Figure 3.7. The gateway DAPs are deployed along two virtual rings, where the outer ring has six and the inner ring has two.

In the second method, each ring is fully deployed on a virtual ring before moving onto the next ring, starting from the outermost ring. As shown in Figure 3.8, the deployment is different from that using the first method. While the gateway DAPs are also deployed along two virtual rings, the second method deploys just one on the inner ring. Apparently, the outsider ring first method will provide a better level of fairness to the customers that are further away from the concentrator. However, more gateways on the outsider rings have side effects on the uplink transmission performance, which will be discussed later in this chapter.

3.3.4 Global Uplink Transmission Power Efficiency

Many researches have considered individual power efficiency (e.g. for DAP , (bits/joule)) for each node in a multiaccess system. Most of them applied noncooperative game theoretical approaches where each player achieves its maximum power efficiency selfishly. However, that approach cannot achieve the maximum social welfare (or the global uplink transmission power efficiency). The global power efficiency is defined as the ratio of total effective uplink transmission rate to the total transmission power. With a given topology for gateway DAPs, the problem is described as follows:

(3.40)

such that

(3.41)

and

(3.42)

Constraint Eq. (3.41) indicates that the transmitting power for each gateway has an upper bound imposed by the FCC rules (especially using ISM bands). Constraint Eq. (3.42) is for the fairness. As discussed before, all gateway DAPs shall have the same receiving power at the concentrator. Without this fairness constraint, this nonlinear optimization problem has extra parameters () and would thus be harder to solve. Nonetheless, with fairness introduced, there is only one parameter to optimize, which reduces the complexity of the problem.

Although the traditional noncooperative game theoretical approach did not have the constraint of equal , its Nash equilibrium was derived with a uniform such that [72–75]. In practice, maximizing individual power efficiency cannot achieve global power efficiency. Assuming , the relationship between global power efficiency and receiving SINR as well as the relationship between global transmission rate and are illustrated in Figure 3.9. From the figure we can see that:

• The global transmission rate increases with respect to SINR. However, the marginal increase will decrease as SINR goes higher.
• A maximizer of the global power efficiency exists. The maximizer does not necessarily represent the optimal SINR that can support the data transmission rate.
• The maximizer achieved by noncooperative game theoretical approach will be off from the global maximizer. It requires a higher SINR, which benefits the transmission rate.

To find optimal solution to global power efficiency, we propose an algorithm as illustrated in Algorithm 3.1. Let be the set of power usages of each DAP. Let be the number of iterations, and be the resolution of each iteration. In each iteration starting from and ending at , there is one maximizer to be found. In the next iteration, the algorithm updates and . With a given , the computational complexity depends on calculating . Fortunately, calculating is indeed solving a linear equation system of linear equations with unknowns. Its computational complexity has an upper bound at when applying Strassen's algorithm [77] for matrix multiplication. Therefore, Algorithm 3.1 has an upper bound for computational complexity , where .

3.4.1 Evaluation of the Optimal Number of Gateways

Let the noise  dBm, M=100 bits, and . Assume a neighborhood block with  km. We first show the maximum number of gateway DAPs with respect to different maximum receiving power . Given a , an optimal number of gateway DAPs can be found by the solution given in the previous section. As shown in Figure 3.10, with higher , the optimal is higher. However, as discussed before, deploying more gateway DAPs causes lower since we need to achieve geographical fairness. Therefore, it cannot deploy too many gateway DAPs while applying low .

3.4.2 Evaluation of the Global Power Efficiency

The global power efficiency depends on the number as well as the deployment of gateway DAPs. The proposed centralized optimization and the traditional game theoretical approach may achieve different results. In the evaluation, geographical issues are considered is only for the centralized approach, since the game theoretical approach is independent of actual deployment as long as the concentrator can still receive from the furthest gateway DAP at optimal SINR.

Figure 3.11 shows the global power efficiency in bits/joule. In general, the global power efficiency decreases as the number of gateway DAPs increases. From the figure we can see that when , all four approaches considering geographical deployment have a sudden drop in global power efficiency. This is caused by the addition of an extra virtual ring in the deployment. Apparently, there is no sudden performance drop without a concern for geographical fairness. Also, no geographical concern appears to have the highest global power efficiency. This occurs because all the gateway DAPs are deployed at closer distances to the concentrator. In reality, we shall adopt the geographical deployment to achieve fairness. Among the four approaches considering geographical deployment, both of the game theoretical approaches achieve lower global power efficiency compared with the centralized optimization results. The centralized optimization results of two deployments appear to be the same, because the deployments are the same for both deployment methods when except for .

3.4.3 Evaluation of the Global Uplink Transmission Rates

In this evaluation, we show the global uplink transmission rates achieved by the proposed approach in comparison to the results achieved by the traditional game theoretical approach.

The results are shown in Figure 3.12. As we can see, the proposed centralized optimization approaches, denoted by “global” in the figure, would achieve the same results regardless of geographical deployments. It is because the global uplink transmission rate depends solely on given the number of gateway DAPs. As long as the furthest gateway DAP is able to achieve with the same , the global uplink transmission rate will remain the same. As a comparison, the global uplink transmission rates achieved by the traditional game theoretical approach are higher than those achieved by centralized optimization. This is due to the higher achieving Nash equilibrium in game theoretical approaches (as shown earlier in Figure 3.9). While not shown in this figure, even the game theoretical approach will have a decreasing marginal increase in the global transmission rate. More importantly, we can see that a maximizer exists when applying global optimization. Therefore, an optimal number of gateway DAPs can be determined accordingly. The results also show that if increased service is needed for more customers, the NAN uplink transmission performance can be enhanced easily by increasing transmission power of each gateway DAP. There is no need for a hardware upgrade in this structure.

3.4.4 Evaluation of the Global Power Consumption

In this evaluation, we show the global power consumption of the gateway DAPs with different approaches. The results are given in Figure 3.13.

We can see that with no geographical consideration, the global power consumption is the lowest. This is because when no deployment issue is considered, the gateway DAPs are actually deployed closer to the concentrator, resulting in lower power consumption. Moreover, the game theoretical approaches have slight higher global power consumption due to their correspondingly higher .

3.4.5 Evaluation of the Minimum Cost Problem

The solution to the minimum cost problem is to find the sufficient size of solar panel and capacity of battery for each DAP to survive the designed life cycle. The transmission power of a gateway DAP is determined by solving the maximum global power efficiency problem after finding the optimal number of gateway DAPs. The transmission power of a normal DAP is a constant value set for Wi‐Fi transmissions. With a given transmission power , the key factors of the minimum cost problem are the length of life cycle as well as the estimated worst‐case scenario . This evaluation is to show the relationships between those factors. Without loss of generality, let , per Wh, and per unit solar panel for the maximum 1 W charging rate. With , evaluation is performed with . In addition to that, when , evaluation is also performed with . Different settings can be easily applied to set other benchmark evaluations.

First, we evaluate the impact on total cost (the objective function) with respect to different values of . The results are given in Figure 3.14. As we can see, either higher or higher will increase total cost for a DAP, since it will need a larger battery and larger solar panel to be self‐sustaining over a longer and harsher life cycle.

Then, we evaluate the impact on battery capacity with respect to different values of . The results are given in Figure 3.15. As we can see, a larger battery is required with a longer life cycle and higher transmission power.

The impact on solar panel size is shown in Figure 3.16. Note that the solar panel size is the same when and . Although the battery capacities are different, the charging rate is high enough to handle the situations.

Finally, we show the impact on charging threshold in Figure 3.17. As it shows, with a higher , the charging threshold increases. However, with a higher , the charging threshold decreases. On one hand, more capacity remaining in the battery is required to survive a longer period with bad weather. On the other hand, if the required life cycle is longer, then the battery must reduce its charging frequency to slow down the deterioration of that battery.