OPTIMIZATION OF INDOOR WIRELESS COMMUNICATION NETWORK LAYOUTS Martin D. Adickes1, Richard E. Billo2, Bryan A. Norman2, Sujata Banerjee3, Bartholomew O. Nnaji2, and Jayant Rajgopal2 1
Symbol Technologies 401 Hackensack Avenue Hackensack, NJ 07601 2
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Department of Industrial Engineering Department of Information Sciences and Telecommunications University of Pittsburgh Why This Paper is Important
This paper discusses a methodology for placing transceivers in Radio Frequency Data Communication (RFDC) implementations. RFDC is a critical component of many automated applications for which industrial engineers are typically responsible. For example, in warehouse management systems, it is often used to track product inventory levels.
In Manufacturing
Execution Systems, RFDC aids the automation of labor tracking, work-in-process tracking, and equipment downtime reporting.
These systems are also integral to such applications as
scheduling, cost accounting, tool tracking, and fixed asset tracking. A predominant problem in successful implementation of RFDC applications is the quick and efficient determination of transceiver placement such that effective radio communication can take place. This research addresses this problem through the development of a computerized layout simulation system incorporating heuristic optimization methods as the placement engine for transceivers. The effectiveness of this layout methodology is demonstrated by comparing it with the current method of utilizing manual site surveys and by comparing it with other placement methods. Results are also presented for locating transceivers in several actual facilities.
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OPTIMIZATION OF INDOOR WIRELESS COMMUNICATION NETWORK LAYOUTS
Martin D. Adickes1, Richard E. Billo2, Bryan A. Norman†2, Sujata Banerjee3, Bartholomew O. Nnaji2, and Jayant Rajgopal2 1
Symbol Technologies 401 Hackensack Avenue Hackensack, NJ 07601 2
Department of Industrial Engineering 1048 Benedum Hall University of Pittsburgh Pittsburgh, PA 15261
[email protected] or
[email protected] 3
Department of Information Sciences and Telecommunications 749 SIS Building University of Pittsburgh Pittsburgh, PA 15260
† Author to whom correspondence should be addressed.
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Abstract Radio Frequency Data Communications (RFDC) technology is a critical component of many automated applications for which industrial engineers are typically responsible. For example, in warehouse management systems, RFDC is often used to track product inventory levels through the Receiving, Put-Away, Picking, and Shipping operations. The current rapid growth in RFDC devices and applications has given rise to a number of challenging implementation issues. A predominant problem in successful implementation of these applications is the quick and efficient determination of transceiver placement such that effective radio communication can take place. This research addresses this problem through the development of a computerized layout simulation system incorporating heuristic optimization methods as the placement engine for transceivers. This method is effective for producing good transceiver placements. The effectiveness of this unique automated layout methodology is demonstrated by comparing it with the current method of utilizing manual site surveys and by comparing it with other placement methods. Additionally, the methodology is also tested in several existing facilities.
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Introduction
Radio Frequency Data Communication (RFDC) is an Automatic Data Capture (ADC) technology experiencing phenomenal growth in both technology and applications development. The market is anticipated to grow at an annual rate of 24.3% for the next five years [1] with applications in both service and manufacturing settings. An RFDC system can be described as any system that communicates data over a radio transceiver between a host computer and a data input source such as data terminals, keyboards, bar codes, magnetic stripe cards, radio frequency identification tags or other wireless computers.
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RFDC technology is a critical component of many automated applications for which industrial engineers are typically responsible. For example, in warehouse management systems, RFDC is often used to track product and inventory levels through the Receiving, Put-Away, Picking, and Shipping operations [2]. In Manufacturing Execution Systems, RFDC aids the automation of labor tracking, work-in-process tracking, and equipment downtime reporting [3,4]. These systems are also integral to such applications as scheduling, cost accounting, tool tracking, and fixed asset tracking. One of the results of the rapid growth of RFDC has been a realization that current methods to determine the optimum locations of radio frequency transceiver transceivers within a facility to meet coverage and throughput requirements are unnecessarily costly, time-consuming, and inaccurate. A large body of work has been amassed over the years in an attempt to quantify and characterize the properties affecting RF propagation. However, the equations governing these properties are complex and are difficult to apply in actual industrial environments due to the complex menagerie of potential sources of environmental interference such as competing radio signals, electromagnetic emissions, and physical obstructions that can deflect or absorb a signal. Such factors have made decisions of transceiver placement based solely on a purely analytical basis impractical at this time. Due to the difficulty in determining transceiver placement analytically, it has usually been done by conducting a manual site survey. With electronic monitoring equipment such as spectrum analyzers, electromagnetic emissions are identified and measured as an RF engineer walks throughout the facility. Using this information, the engineer attempts to identify the locations for the transceivers that will minimize the disruption of service. Unfortunately, without a full understanding of all the potential interference sources, the results of this task are often
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inaccurate. If an inadequate number of transceivers are placed at the site or their locations are inappropriate, then dead spaces, areas where there is no transmission coverage, are often found after the RF network is in place. To avoid these problems, RF engineers often over-saturate a site with transceivers early in the network design phase of the project. For large sites, these extra units may add excessive costs, while providing little added value to the RF network. In addition to their inaccurate nature, site surveys are expensive to perform, require sophisticated electronic monitors, and have the potential for disrupting normal operations at the site. 2
Research Statement This research describes a methodology and placement tool for identifying the optimal
number and location for transceivers within facilities. To date, no research has been conducted to optimize and automate this process. Using established propagation models and knowledge of the facility, this research describes coverage algorithms and heuristic optimization algorithms to optimize the location of transceivers within any type of facility. Specifically, coverage for the transceivers is modeled as a geometric circle covering problem; the optimal locations of the transceivers are then found using a genetic algorithm. Geometric circle covering algorithms provide a mechanism to place a number of circles over an area in such a manner as to completely cover the area with the minimum number of circles. In the present problem, circles represent transceivers emitting omnidirectional radio waves. The genetic algorithm then attempts to optimize transmitter placement by successively placing the circles in better locations. The genetic algorithm uses three objective functions to evaluate placement solutions. These include functions to maximize facility coverage, maximize the data transmission rates to meet the facility data throughput requirements, and maximize the average signal strength across the facility.
In addition, the placement tool addresses both passive
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interference (e.g., physical obstructions such as walls and equipment) and active interference (e.g., electromagnetic fluctuations) in determining effective placement solutions. If an RF engineer had such a tool to develop a placement scheme for transceivers prior to actually visiting a site, many of the current problems encountered during the process could be minimized or even eliminated. Use of an effective placement methodology and tool would provide the RF engineer with the following advantages: 1. The capability to optimize transceiver placement with respect to coverage and cost considerations. 2. The ability to quickly and accurately determine placement positions for transceivers prior to visiting the site. A majority of the time involved in the site survey process is spent physically placing and analyzing the locations of the transceivers.
Accurate development of a
placement solution prior to visiting the site will result in a significant reduction in the time the engineer needs to spend at the site performing the installation. 3. Having characteristic information regarding the site where the transceivers are to be installed (e.g. obstructions, active interference sources, building design) reduces the chances of placing transceivers in a manner that allows dead spots or areas with less than desirable communication coverage. 4. Performance of the system can be predicted for the number of transceivers needed or the level of coverage desired. 5. Alternative optimal transceiver layouts could be identified and analyzed. In many situations, there is more than one than one way of configuring the transceivers to ensure adequate coverage. In these instances, additional criteria can be evaluated in order to make the final placement decision.
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6. New or changing information regarding the characteristics of the facility could quickly be incorporated and analyzed to help maintain appropriate coverage. 3
Literature Review
In order to model the transceiver placement problem it is necessary to understand some of the basic properties of RF signal transmission and these properties are discussed in this section. We also discuss previous research for the transceiver placement problem. 3.1
Wireless Channel Characteristics
Wireless radio channels exhibit significantly complex behavior as compared to wired channels. In free space, the combined effect of reflection, diffraction and scattering causes electromagnetic waves to travel across many paths on their way from the transmitter to the receiver.
The
interaction of these waves at the receiver combined with any other active/passive interference sources cause the signal to fluctuate or fade, sometimes quite quickly.
In an attempt to
characterize these interactions, two types of propagation models are typically built [5], using primarily empirical techniques [6]. Propagation models that predict the average signal strength for an arbitrary transmitter-receiver distance are called large scale propagation models. Those that attempt to characterize the rapid fluctuations of the signal over very short distances or time are called small scale or fading models. Small scale propagation models are important for modeling continuous transmission applications such as a cell phone conversations, while large scale path losses are more appropriate for short, discrete transmission applications, such as those found in factory applications or indoor environments [7]. This is because many of the devices used for these applications employ the interference rejection and immunity techniques to counter rapid, localized signal fluctuations [8].
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Indoor propagation models need to account for the obstructions inside the building under consideration, in addition to reflection, diffraction and scattering. Because the makeup and specific nature of individual buildings is so unique, Molkdar [9], in a 1991 survey, attempted to develop a classification of buildings that disregarded the detailed structure of any particular type of building. His review of the literature suggested that structures could be classified into broad categories described in Table 1. Buildings in each of these categories exhibit similar propagation loss characteristics.
Rappaport [7] did some additional work with respect to factories and
developed four sub-categories by which buildings could be classified: line of sight with light surrounding clutter, line of sight with heavy surrounding clutter, obstructed path with light surrounding clutter, and obstructed path with heavy surrounding clutter. Additional work by researchers has gone further to include propagation losses incurred by common building materials and multiple floors of a building [10,11]. Table 1. Building Classifications Category 1 2 3 4 5 6 7 8
3.2
Description Residential house - suburban area Residential house - urban area Office building - suburban area Office building - urban area Factory with heavy machinery Other factories, sports halls, exhibition centers Open environment - Airport, Railway station, etc. Underground environment - subway, underground street, etc.
Propagation Loss Models
Numerous models and methods for modeling propagation loss have been proposed and developed over the years, as detailed in the comprehensive survey and tutorial performed by Hashemi in 1993 [12]. This work explains and references over 280 references to principles,
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concepts and work done with respect to indoor radio propagation. Most of the references and work Hashemi cites are with respect to the mathematical and statistical modeling done by researchers on individual characteristics of propagation losses. Another way that propagation losses can be modeled utilizes ray tracing techniques which characterize the multipath characteristics of a signal as it travels through an environment. Kreuzgruber [13], for example used a ray splitting model incorporating diffraction characteristics to model indoor propagation. Schoeberl [14], in his work, modeled indoor propagation losses using a combination of ray tracing and Monte Carlo simulation, while Driesseu [15] describes a ray model incorporating geometric optics with antenna and polarization effects. Ray tracing has been found to be quite accurate though the technique can be quite slow [16], particularly for interactive site planning tools. Both theoretical and measurement based propagation models indicate that average received signal power decreases logarithmically with distance, and can be described using the equation: d N PL(d )[dB] = PL(d 0 )[dB ] + 10a log10 + ∑ B[dB ] d 0 i =1
(1)
where a is the path loss attenuation factor derived from tables or measurement, d is the distance separating the two units, d0 is a reference distance from the transmitting antenna and B is the amount of attenuation the signal undergoes as it passes through a passive obstruction [5,17]. The actual amount of attenuation depends on the obstruction type and frequency. Although a first order approximation, researchers have found that in many cases it provides accurate characterization information, and have used it successfully to characterize indoor propagation losses [15,18].
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3.3
Previous Transceiver Placement Methods Despite the work done on modeling of propagation losses, development of models that
aid in the placement of transmitters on factory floors has been limited. Panjwani et al. [14] have developed an interactive method for placing transmitters in multi-floored indoor environments based on ray tracing techniques coupled to the path loss model described in (1). Although several propagation models are considered in the software, the system is a manual placement solution. The user identifies initial transceiver locations on the screen and the system calculates the coverage. The user must then identify alternative locations in successive attempts to increase coverage. There is no capability to find an optimal solution with this tool, and there is no automation capability to move transceiver locations. Although such an approach may work for small layouts where only one or two transceivers are required, this manual placement approach quickly becomes unwieldy when a larger number of transceivers are required. Sherali [20] developed a set of non-linear programming models based on the Hooke and Jeeves’ method, quasi-newton, and conjugate gradient search algorithms to seek the optimal location of transmitters to serve specified distributions of receivers. None of his approaches were able to generate repeated solutions, however, and his research stopped short of extending to handle disconnected or discrete areas where transmitters could be located. Tang [18] utilized a hierarchical genetic algorithm as an approach for placement of multiple transmitters in indoor environments, but limited his placement of transmitters to a small subset of locations, and did not incorporate either required data rates or active interference as a factor in transmitter placement. Stamatelos [21] utilized neural networks and simulation to develop an indoor wireless network development tool to aid in transmitter placement, but focused on the use of adaptive antenna arrays as a method of increasing antenna coverage.
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Transceiver Placement Problem Methodology
The problem of locating transceivers was modeled using a genetic algorithm that is based on representing the problem as a circle covering problem. Section 4.1 discusses the relationship between the circle covering problem and the transceiver location problem. Section 4.2 discusses a methodology for determining the coverage area for a transceiver. Section 4.3 describes a method for determining an initial estimate of the number of transceivers that will be needed. Section 4.4 discusses the genetic algorithm used to determine transceiver location. 4.1
Circle Covering Representation of the Problem
The problem of placing transmitting units is similar to the geometric circle covering problem. In this problem, the goal is to place n circles over an area in such a manner as to completely cover the area with the minimum number of circles possible.
This area can be characterized as:
n U Ci I A where n is the number of circles covering an area, Ci is the ith circle in question, and i =1 A is the total area of the region desiring coverage. Circles are allowed to overlap, and can be placed so that they are either completely contained within or allowed to extend beyond the borders of the region of interest. Many problems dealing with circle coverings have been proven by mathematicians to be unsolvable [22], and solutions for cases involving placement of any more than a trivial number of circles do not exist [23]. Zahn [24] realized that the coverage of a circular area A by a configuration of circles C1, C2, …, Cn could be uniquely determined by specifying a vector of (x,y) coordinate pairs Ψ = (x1, y1, x2, y2,…, xn, yn,) where (xi, yi,) denotes the center of the circle Ci. This vector Ψ completely determines the coverage of the n circles with respect to A, and can be used as the basis for maximizing some function F(Ψ) over a bounded area. Due to the difficulty of determining the
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total area covered by the union of all of the circles, his approach was to discretize the area being covered by constructing a grid over the area A. The estimate for the area of coverage within A is described by the number of grid points, n1, lying inside the boundary of A. The area covered by the circles is described by the number of grid-points, n2, that lie in both A and at least one of the covering circles. F(Ψ) was approximated by the quotient n2/n1. We also discretize the facility floor area to facilitate calculating coverage. One meter square grids were used in the test cases described in Section 5 although larger or smaller grid sizes can be chosen based on the specific placement environment. 4.2
Estimating Transceiver Coverage
The primary difference between the circle covering problem and the transceiver location problem is that the coverage area of transceivers is not strictly circular because there are sources of interference that affect the transceivers’ signal (see Figure 1). Therefore, it was necessary to develop a methodology for determining the area that the transceivers actually cover.
This
methodology had to account for the various ways that a signal can weaken or distort over distance. Although the coverage region of a transceiver will initially be circular, obstructions placed in the path of the radio wave will attenuate it and limit the distance it can travel, thus perturbing the shape of the coverage region. In a similar fashion, noise, although not physically attenuating the signal degrades its quality in such a manner as to limit the effective transmission range. To meet these requirements, a Transceiver Coverage Heuristic (TCH) was developed. The objective of TCH was to completely characterize a set of discrete areas that fall within the transmission range of a transceiver. TCH evaluates regions between a transceiver and the edge of the coverage region along a predefined path. This path corresponds to a directed RF signal of
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a known frequency and power. The signal is then monitored along the path until it’s strength drops below a specified threshold. The signal may degrade due to traveling a long distance, encountering obstructions, or encountering other interference sources. Once the signal strength drops below the threshold, the path is terminated, and a new path created and evaluated in a similar manner. These paths are swept completely around the transceiver, so that a coverage region is eventually defined and evaluated.
a. Idealized circular transceiver area.
b. Actual coverage areas due to obstructions
Figure 1. Idealized versus actual coverage area.
4.3
Indicates transceiver placement.
Initial Estimation of the Number of Transceivers Needed
To facilitate determining the optimal number of transceivers needed for the coverage area it was useful to determine an estimate of the number of transceivers needed for coverage. The heuristic developed to solve this problem is called the Initial Covering Heuristic (ICH).
First, a
conservative estimate must be found that represents the attainable coverage area of a single transceiver. For an isotropic antenna source, a coverage circle (C) will be generated with a corresponding diameter. By inscribing the largest square possible inside C, call it a coverage square (S) with side length s, a conservative representation of the transceiver coverage area is obtained. Then S can be used to tessellate the coverage region which provides an initial estimate
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on the number of transceivers needed. The tessellation process begins in the upper left corner and proceeds across the coverage region to the right side of the coverage region. Then the process continues by covering strips of height s until the all the necessary area is covered. Figure 2 provides an example of the ICH. Figure 2a shows the facility floorplan and the shaded areas represent the areas that require coverage. Figure 2b shows how the facility will be covered using three strips based on the size of S. Figure 2c shows the result of the tessellation process for the first row. Figure 2d shows the final result of the tessellation process and how the initial estimate would be 10 transceivers. Note that the ICH makes no assumptions about the size or shape of the region to be covered. Regions to be analyzed are not limited to simple closed, rectangular shapes. Curved perimeters and discontinuous regions inside an area to be covered can also be evaluated by ICH. 4.4
The Genetic Algorithm Optimizer (GAO)
The ICH and TCH were used in conjunction with a genetic algorithm methodology to optimize transceiver placement. Genetic algorithms (GAs) are population-based heuristic optimization techniques employing search procedures based on mechanics of natural selection and genetics. In a GA, an initial set of solutions, called chromosomes, is generated via a random mechanism, evaluated using a fitness or objective function and used as a staring point for developing potentially better solutions through the mechanisms of crossover and mutation. Since their inception, GA’s have seen tremendous growth as a research area, and have been successfully applied to numerous optimization problems. Advantages of genetic algorithms include their ability to handle a wide variety of functions (e.g. non-linear, continuous, discrete, mixed, constrained), and the ability to solve problems in a domain independent manner, using only an
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evaluation of the objective function. Excellent texts dealing with the specifics of GAs can be found in Goldberg and Michalewicz[25,26]. a.
b.
S
c.
1
d.
2
1 3
2
4
5
3
4
7
8
6
9
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Figure 2. Initial Coverage Heuristic Example
We encoded the transceiver placement problem for the GA as a set of n (x,y) coordinate pairs {(x1,y1), (x2,y2), …, (xn,yn),}, where (xi,yi) represents the location of an individual transceiver. Individual genes in the chromosome are represented by a pair of coordinates representing the location of the transceivers. The ICH provides an initial estimate of the number of transceivers, N, which are needed to cover a facility.
A population of solutions, each
containing N randomly placed transceivers is then generated. Each solution in the population is then evaluated using TCH. To evaluate a transceiver configuration, the overall coverage area was discretized into an X row by Y column grid of equal area squares, each of which is assigned to a unique transceiver
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(the transceiver that transmits the strongest signal to that square). Note that in general, there may be portions of the overall coverage area where coverage might not be required (e.g., walls and unusable areas). Define [x,y]
= identity of the square in row x and column y, where x=1,2,..,X and y=1,2,…,Y
A
= {[x,y] | coverage is required at the location [x,y]}
T[x,y] = identity of the transceiver to which location [x,y] is assigned; [x,y]∈A Three fitness measures were used to determine the quality of a particular transceiver placement. The first objective, f1, determined the percentage of the area in the facility covered by a particular configuration of transceivers. A point [x,y] is considered to be successfully covered by the transceiver T[x,y] to which it is assigned, if the path loss of the signal from T[x,y] to the location [x,y] is no larger than a specified threshold value. Define Sxy
= 1 if [x,y]∈A and [x,y] is successfully covered by T[x,y]; 0 otherwise
Then the first objective is to
∑∑ S xy Maximize f1 =
x
y
| A|
where |A| denotes the cardinality of set A. Note that f1 is the fraction of the required coverage that is actually attained by the proposed placement scheme. From an implementation standpoint, the goal of the RF engineer is to make f1 = 100%. A second objective function, f2, calculates the average regional capacity, or throughput, that a transceiver can achieve over parts of the required coverage area for which a specified minimum capacity threshold must be attained. In the current research we utilize an idealized capacity model based on the Shannon-Hartley law [6]. Define
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N
= {[x,y]∈A | location [x,y] also has a capacity threshold specified}
Cxy
= 1 if [x,y]∈N and the capacity of [x,y] with respect to T[x,y] exceeds the threshold; 0 otherwise
Then the second objective is
∑∑ C xy
Maximize f2=
x
y
|N |
The third objective, f3, relates to the average signal strength across all points that require coverage. Define Gxy
= strength of the signal between location [x,y] and T[x,y] if [x,y]∈A; 0 if [x,y]∉A
The third objective is
∑∑ Gxy Maximize f3 =
x
y
| A|
The three objectives are combined using a Pareto ranking based on their importance in the development of the overall solution. Coverage was considered the most important objective in determining the value of a solution, followed by minimum capacity requirements over some predefined area, then average signal strength over the entire facility. Thus, if we consider the following two solutions M1 and M2 with objective functions f1, f2, f3 and f′1, f′2, f′3 respectively. Solution M2 is considered preferable to M1 if and only if one of the following conditions holds true: Condition I:
f1′ > f1
Condition II:
( f1′ = f1 ) and ( f 2
Condition III:
( f1′ = f1 ) and ( f2′ = f2 ) and ( f3′ > f3 )
)
< N t and
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( f 2′
> f2
)
where Nt is the average regional capacity threshold. To determine an individual fitness for each solution in the population we utilize preferential ranking, which has been shown to be an effective method of assigning fitness to problems containing multiple objective functions [8,18]. The population is first sorted, and solutions ranked from best to worst according to the criteria stated above. We then assign a fitness to each solution using rank (i ) − 1 f i = bl + (bu − bl ) N −1 pop
(2)
where fi is the fitness of the solution, rank(i) is the rank position of solution i in the ordered population, Npop is the size of the population, and bu and bl are the upper and lower limits of fitness, respectively. For this research bu was set to 1, and bl was set to 0.1 so that all solutions would have some chance of being selected for inclusion into the breeding pool. Finally, the fitnesses of all solutions having the same rank are averaged so that each will be selected with an equal probability. Once a fitness has been calculated for each solution in the population, the total fitness F of the population is calculated from
N
F = ∑ fn
(3)
n =1
where n is the size of the population and fn is the fitness of the nth member of the population from (2). The probability of selection pn for each solution can then be found from
pn =
fn F
(4)
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Selection The GAO developed for this research utilizes a proportional selection scheme (or roulette wheel selection) as the mechanism by which solutions are selected for inclusion into the GA breeding pool. The breeding pool is constructed by drawing random samples with replacement from the current population where the probability of selecting an individual is directly proportional to pn. Parents are selected from the breeding pool to mate or undergo crossover using tournament selection with size 5. The GAO starts the mate selection process by randomly selecting a single solution, call it parent 1, and removing it from the breeding pool. Next, five candidate solutions are randomly selected from the breeding pool.
The best of these five
solutions, as determined by its fitness, mates with parent 1. After mating, all selected solutions are replaced into the breeding pool and given a chance to participate in the next mate selection. Mating The GAO developed in this research generates a new population of solutions based on a combination of elitist selection and breeding of new solutions using crossover and mutation. Population size is held constant between generations and was fixed to a size of 30 solutions for this research. The top two solutions of the previous generation are automatically selected for inclusion in the next generation. All remaining members are chosen for inclusion by choosing two parents based on the selection mechanisms outlined previously and mating them to produce two children. All four solutions are then evaluated, rank ordered according to fitness, and the best two passed into the new generation.
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Figure 3 shows an example of the crossover mechanism employed in this research to generate offspring for evaluation. In general, consider the pair of solutions Sa = [(x1,y1)(x2,y2)…(xI,yI)] and Sb = [(x1,y1)(x2,y2)…(xI,yI)]. Crossover By Location (2,9)
(2,9) (8,7)
(8,7)
(6,5) (3,2)
(6,5) (3,2)
Sa = (2,9) (6,5)
(2,9)(8,7) s
Sb = (3,2 )(8,7)
(3,2)(6,5) s
Figure 3 The GAO Crossover Mechanism Each solution has I pairs of coordinates that correspond to the placement of a transmitters on the facility floor. Then parameterized uniform crossover, with a probability based on the average Pareto fitness of the previous generation, is performed on the two parent solutions. Note that crossover is based on exchanging the pair of coordinates that locate a transmitter, not the individual x or y coordinate. Mutation All members of the population are subject to the mutation process, with the exception of those members marked as elitist solutions. Mutation is dynamic, and in a manner similar to the breeding process uses the average Pareto fitness of the previous generation as a basis for determining how much a selected part of a solution can change. The mutation process operates at the coordinate level of the solution, and is governed by three values: the mutation threshold, mutation range and search threshold. The probability that a particular coordinate will be selected for alteration is governed by the mutation threshold, which has been set to 10% for this research.
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The mutation range determines the magnitude of the alteration being applied to the coordinate selected for mutation, and is determined using
M r = INT (k ( F * R ) + 1
(5)
where Mr is the mutation range, INT is a function returning the integer portion of a real number, k is a user-defined scaling constant, F is the average Pareto fitness of the previous population, and R is the maximum effective transmission range of the transmitter. As the average fitness of the generation increases, the allowable magnitude of the mutation change is decreased, thus causing the mutation process to focus more on the neighborhood surrounding the original coordinate location. The final parameter, called the search threshold, works in conjunction with the mutation range to ensure that all areas of the solution space have some probability of being searched. The search threshold, or Ms, dictates the probability that a coordinate selected for mutation will mutate within the region defined by (5), or over the entire range of valid x or y coordinates. For this research, Ms was set to a value of 0.3, meaning that 30% of the time a coordinate chosen for mutation would mutate to any legal value defined by the limits of the search region, while 70% of the time the mutation would occur within the range set by Mr. The flowchart for the GAO methodology used for this research is shown in Figure 4. Note that the GAO would initially be run using a number of transmitters based on ICH. Assuming 100% coverage could be attained, the number of transmitters would be reduced by one and the GAO would be run again. This process would continue until the performance criteria are not satisfied, e.g. 100% coverage cannot be attained with acceptable capacity.
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Generate ICH Solution
START
Reset For Next Run
Initialize GO Data Structures
Generate Random Population
Evaluate Population
Acceptble Solution Found?
YES Record Results
NO
YES Terminate Run?
NO Generate Breeding Pool
Breed New Solutions
Generate New Population
Apply Mutation
Figure 4 GAO Flowchart
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Using these three objectives, the GAO begins by finding a solution using N transceivers that provides complete coverage. Then the GAO is rerun using N-1 transceivers. This process is repeated to find the smallest number of transceivers that provides complete coverage for A. 5
Model Validation
Validation was conducted by examining how the GAO performed with regard to accurately determining capacity and coverage. This was done by examining different transceiver location strategies in actual facilities. Measurements for signal strength were recorded using software provided by the manufacturer of the transceiver equipment. This software gave an indirect measure of the signal strength at any particular point via a value called a Received Signal Strength Indicator (RSSI). This is a proprietary software package used by RF engineers of a major company dealing in RF equipment to conduct site surveys.
Unfortunately, direct
conversions to capacity values were not possible. However, an indication of the goodness of the solution can be obtained by comparing the values of the GAO calculated capacity with the RSSI. By comparing the values the GAO calculates at various points in the facility to those generated by actual measurements at the same points, an indication of how well the GAO and physical measurements correlate can be calculated. To do this a sample correlation coefficient was calculated using the GAO calculations and RSSI values, respectively, taken at various points in the facility. A comparison of the two sets of data yields a correlation coefficient of 0.85, indicating a strong positive linear relationship between the physical measurements of the signal strengths taken in the facility and the signal to noise ratios calculated by the GAO. The GAO is therefore behaving in a manner consistent with measured expectations. This data also indicates that our choice of path loss models with parameters based on facility characteristics closely reflects real signal propagation.
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Differences in the readings can be attributed to a number of reasons. First, the software used to display the RSSI value does not give an aggregate reading at the end of a sample. The user must visually estimate the strength from the numbers as they scroll across the screen. In most cases the numbers remained fairly constant, but periodically, there were minor fluctuations that introduced some error. Second, RSSI values were displayed in 1-unit intervals, as opposed to the GAO calculations, which calculated a real number for each location. Finally the RSSI value measured the actual signal strength at the location.
Therefore, any change in signal
strength due to large or small scale fading will be reflected to some extent in the RSSI reading. 6
Model Effectiveness
The effectiveness of the GAO in generating solutions was tested in three different ways. The first was to compare the GAO with a solution methodology proposed in the literature on a published test problem.
The second was to compare the effectiveness of the GAO search
methodology by comparing it to an exhaustive enumeration on the same published test problem. The third method compares the GAO to a series of site surveys and alternative manual placement methods in four warehouses. 6.1
Comparison of GAO to Literature Results
The GAO was compared to results of a genetic algorithm as developed by Tang [18]. Figure 5 illustrates an office facility described in [18]. This facility represents an environment where the only sources of interference are passive, and consist of floor to ceiling walls of two different types. Any square containing a number indicates that a wall passes through that square and an RF signal passing through it must be attenuated by an appropriate amount. Squares containing the number 1 indicate walls that attenuate signals by 3 dB, while squares containing the number 2 indicate walls that attenuate signals by 6 dB. Dimensions of the facility measure 75 meters
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wide by 30 meters high, with each displayed square representing one square meter of facility floor. Two transmitter configurations were examined in this process. The first configuration verified the results of placing two transmitters, each with a power loss threshold of 100dB, into the facility. The second example was similar, verifying the results of placing five transmitters, each with a power loss threshold of 80 dB into the facility. Different transmitter configurations were evaluated for coverage, average signal strength loss, and average maximum signal strength loss over the entire facility.
Because capacity (required data rates) and active interference
sources were not addressed in Tang’s example [18], only facility coverage and average facility signal strength metrics are compared. 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2
2 2
1 1 1 1
2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 1 1 1 2 1 1 2 1 1 1 1 2 1 1 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 1 1 1 2 2 2 2 2 2
2 2 2 1 1 1 2 2 2
2 2 2 1 1 1 2 2 2
2
2 2 2 2 2 1 1 2 2 2 2 2 1 1 2 1 1 2
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2
2 2 2 1 1 1 2 2 2
2 2
2
2 2 2 1 1 1 2 2 2
2 1 1 1 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 1 1 1 2
2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 2 2 1 2 2 1 1 1 2 2 1 1 2 2 1 1 1 1 1 1 1 1 2 2 1 1 1 2 2 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 2 2 1 1 2 2 1 1 1 1 1 1 2 1 1 1 2 1 1 1 1 2 2 1 1 1 1 2 2 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 1 1 1 2 2 2
2 2 2 1 1 1 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 1 1 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
Figure 5 Tang(44) Office Layout Table 2 compares the results obtained by the GAO to those of Tang [18] with respect to facility coverage, average signal loss and maximum average signal loss when two and five transmitters, respectively, were placed on the facility floor.
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As can be seen from Table 2, both Tang’s GA and the GAO were able to find a solution that provided 100% coverage over the facility. However, the GAO found a solution where the average path loss experienced by the transceivers was less than the results calculated by Tang, meaning that average signal strength over the office floor was stronger. The GAO was also able to track the path of each signal to almost the threshold of the transceiver’s sensitivity, unlike Tang’s calculations, which stopped several decibels short. Table 2 Comparison of GAO Results With Tang’s Results TWO TRANSMITTER PLACEMENT (Maximum Acceptable Path Loss = 100 dB) Tang Results GAO Results Total Coverage Average Path Loss
100% 69.59 dB
100% 68.26 dB
FIVE TRANSMITTER PLACEMENT (Maximum Acceptable Path Loss = 80 dB) Tang Results GAO Results Total Coverage Average Path Loss
6.2
100% 61.42 dB
100% 60.23 dB
Exhaustive Enumeration Test
In order to determine if the solution generated by the GAO for the placement of two transceivers represented the optimal solution for the entire facility, an exhaustive enumeration was performed of all legal possible transceiver placement combinations for the two transceiver placement problem. Table 3 summarizes the results of the exhaustive enumeration. Only one solution was identified as optimal, which corresponded to the same point that the GAO found. These figures indicate that only 3% of all legal placement combinations result in acceptable solutions (have 100% coverage), with only .03% falling within 1 dB of the optimum average path loss. Thus, it is clear that this is a complex search space. Because it requires two seconds to evaluate each transceiver location combination, the enumeration process requires 567 hours of computer time.
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Because the problem search space size grows exponentially as additional transceivers are added into the solution only the two transceiver problem was solved using exhaustive enumeration. Table 3 Exhaustive Enumeration Summary for Two Transceiver Placement Total number of solutions
1,021,979
Total number of optimal solutions
1
Number of solutions covering entire facility
31,499
Number of solutions covering facility having average facility 4,577 signal strength within 3 dB of optimal solution Number of solutions covering facility having average facility 332 signal strength within 1 dB of optimal solution 6.3
GAO Effectiveness Compared to Site Surveys
In order to test the performance of the GAO and covering heuristics under real-life conditions, four large warehouses ranging in size up to 60,000 square feet in local factories were characterized. In the same manner as RF engineers performing an actual site survey, measurements at each facility location were based on data gathered from repeated transmissions of a message packet of known length. For this testing, each location on the facility floor was examined by sending 100 messages containing 512 bytes of information, and information on the estimated signal strength at each measured location. Results from the GAO and site surveys for the four warehouses are summarized in Table 4. Position A represents the point where, based on the parameters it was given, the GAO placed the transceiver to achieve optimal coverage.
Position B represents an alternative location
identified by the company’s information systems staff and an RF engineer familiar with the fundamentals of site surveys and radio frequency propagation.
In every case the solution
suggested by the GAO provided better coverage to the facility (had less dB loss) than was suggested by the alternative placement. The layout of the first warehouse is shown in Figure 6. From the diagram it is clear that the GAO solution is significantly different than that proposed by
26
the RF engineer and the results in Table 4 demonstrate that the GAO solution is better than the manual placement. This supports the hypothesis that the intuitive manual placement solution is not necessarily best. The GAO overcomes the limitations of manual placement by providing a methodology to search the set of all possible transceiver placement combinations.
LEGEND A = GA Solution B = Manual Placement
- Product Storage - Illegal Areas
B
A
Figure 6. Warehouse 1 and Transceiver Placement. Table 4 Test Results for Semi-Obstructed and Open Facility Environments SIGNAL STRENGTH (dB loss) GAO Alternative Location: A B Facility 1 67.59 69.24 Facility 2 66.33 71.38 Facility 3 66.46 67.73 Facility 4 78.48 80.22 7
Concluding Remarks
This research represents the first systematic effort at formulating the determination of the number of transceivers and their placement as a formal optimization problem. We have been able to develop an optimization scheme for a real problem considering reasonable assumptions, and the results obtained have been field-validated in several application settings. The results
27
demonstrate that our methodology which combines first principles of signal propagation with interference and obstruction data based on actual site characteristics is highly effective for generating better solutions in real environments. The placements were found to be superior to what would have been obtained had the current practice of manual site-surveys been followed, while at the same time being significantly less expensive to obtain. The GAO has also been tested on problems involving capacity constraints and shown to be effective. However, those results are not included here for the sake of brevity. By the very nature of the RF transceiver placement problem, only a few of the vast number of possible solutions can ever be examined with physical placement methods, with no way of accurately assessing the feasibility of a generated solution. This methodology presented here provides an effective mechanism to evaluate large, complex solution spaces specific to transceiver placement environments and suggests multiple alternatives that will meet specific application requirements.
It also expands the concept of multiple concurrent placement of
transceivers by incorporating both active interference sources and capacity requirements into the development of the overall placement equation, as well as characterization of the impact of obstructions. There are very few products that provide the capability of evaluating a facility to determine the placement of RF transceivers and no products are available for optimizing the placement of transceivers. The GAO represents a heuristic optimization technique (genetic algorithms, circle covering heuristics) that provides a complete and more accurate placement solution than what is available with current alternative methods. In the future we will consider several extensions to this research. First, the algorithm will be run using different propagation and capacity models. Second, alternative antenna
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configurations can be considered. In this research all antennae were assumed to be omnidirectional but in reality it may be beneficial to consider the use of directed antennae to provide better coverage to certain areas. Finally, future work will also explore providing coverage with a mix of antennae of different strengths and costs. References 1.
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