Abstract:
Methods for modeling costs of wireless network infrastructure are described. More specifically, the cost contribution models for modeling radioports are described. Various radioport architectures include a constant channel capacity model ( 48 ) and a constant offered load model ( 82 ). Under constraints imposed by a class of dense user networks, such as wireless metropolitan area networks, cost models are shown to exhibit convex cost functions having minimums. Processes for analyzing these cost models are described for determining which radioport architecture, provides a least-cost radioport cost segment to the overall network cost.

Description:
RELATED INVENTION  
       [0001]    The present invention claims priority under 35 U.S.C. §119(e) to: “Modeling and Optimizing Wireless Network Infrastructure Economic Cost,” U.S. Provisional Patent Application Serial No. 60/170,501, filed Dec. 14, 1999, which is incorporated by reference herein. 
     
    
     
       TECHNICAL FIELD OF THE INVENTION  
         [0002]    The present invention relates to cost modeling of communication networks. More specifically, the present invention relates to determining cost structures for radioport architectures.  
         BACKGROUND OF THE INVENTION  
         [0003]    Wireless, or cellular, communications networks are based on the concept of dividing a radio coverage area into units called cells, each of which contains a radio access port, or radioport (receiver/transmitter/antenna combination) that communicates with wireless users within the cell. As users move across the terrain, they move from one cell to another. Their calls are handed off from the cell they are leaving to the cell they are entering, ideally without any noticeable effect. By dividing the service area in this manner, it is possible to reuse the frequencies allocated from cellular telephony many times, thereby increasing the efficient use of the allocated spectrum.  
           [0004]    Wireless communications is a capital-intensive business, and carriers are continuously seeking to reduce costs associated with cellular communications networks. The total system infrastructure cost of a cellular communications network fixed plant can be decomposed into three major elements: switching, interconnect, and radio access. As such, a total system infrastructure cost may be written as: 
             C   tot   =C   sw   +C   in   +C   rad   (1) 
           [0005]    where C tot =total system infrastructure cost, C sw =total switching and control segment cost Mobile Switching Center/Base Station Controller (MSC/BSC), C in =total cost of interconnecting control and radio segments, and C rad =total radioport segment cost. Each cost component is a sum of its elemental costs, such as equipment, land, and facilities.  
           [0006]    Conventional cellular radio access equipment is large and expensive. Land and buildings required to contain the conventional cellular radio access equipment are similarly large and expensive. Therefore, the radioport segment cost, C rad , has traditionally been the largest cost element in cellular systems.  
           [0007]    A trend in wireless communications is towards lower-power, more closely spaced radioports, also known as base stations, access points, and base station transceivers. As radioports become smaller, they also become less costly. In particular, smaller, lighter radioports can be mounted on utility poles or the corners of buildings rather than requiring dedicated sites, buildings, and towers. This trend should reduce the real estate costs associated with the larger dedicated sites, buildings, and towers. A reduction in real estate costs consequently results in a reduction of the radioport segment cost, C rad .  
           [0008]    Many established and developing cellular markets have dense user populations. There are two ways to serve more users within a cellular or microcellular system, the traffic-handling capacity of each cell is increased or more spectrum is used. The traffic-handling capacity improvements are being achieved using advanced technologies such as code division multiple access (CDMA), but these are insufficient, in and of themselves, to provide the additional needed capacity.  
           [0009]    Since the absolute amount of spectrum available for a cellular system is fixed and inelastic, additional spectrum can be gained only through reuse, which means closer spacing of cells than is customary in traditional cellular systems. Indeed coverage radii for a personal communications system (PCS) or another microcellular cell is approximately equal to or less than three kilometers. Accordingly, the smaller, more closely spaced, radioports are particularly useful for serving more users in regions of dense user concentrations. Although more of the smaller radioports are needed, their unit costs will drop such that the share of total costs represented by the radioport segment cost, C rad , will drop.  
           [0010]    Owing to the considerable investment required in a wireless communications network, models have been developed to attempt to optimize the costs of wireless networks. Wireless communications networks are complex systems, and the development of an optimal cost solution for the interconnections of such a complex network is a difficult problem in combinatorial mathematics. However, the problem of designing optimal cost networks has received much study because it is important to the design of networks that they can return a profit to their operators.  
           [0011]    In general, these problems do not possess analytical solutions and are typically attacked using various heuristic methodologies. In turn, these heuristic methodologies are mathematically complex and require significant computational power and time. Due to their complexity and cost, the heuristic methodologies are avoided by practicing network designers. In addition, some of the methodologies, are only useful over a small set of reasonable conditions. Yet another problem with prior art techniques is that many of these methodologies are designed to be used only after the radioports have been specified and designed.  
           [0012]    For the reasons discussed above, many prior art network cost optimization methodologies are not commonly used in the practical design of wireless network infrastructures, which virtually ensures non-optimal topologies.  
         SUMMARY OF THE INVENTION  
         [0013]    Accordingly, it is an advantage of the present invention that a method is provided for determining system architecture for radioports in a wireless communications network.  
           [0014]    It is another advantage of the present invention that the method identifies a cost optimal system architecture for the radioports.  
           [0015]    It is another advantage of the present invention that a cost optimal system architecture is identified that is suited for a dense user topology.  
           [0016]    The above and other advantages of the present invention are carried out in one form by a method for selecting one of a plurality of radioport architectures of radioports in a wireless communication network. The method calls for specifying parameters associated with the radioports, and computing composite powers for the radioport architectures in response to the parameters. Cost structures are determined in response to the composite powers for the radioport architectures, and the cost structures of the radioport architectures are compared to select the one radioport architecture.  
           [0017]    The above and other advantages of the present invention are carried out in another form by a computer-readable storage medium containing executable code for instructing a processor to select one of a plurality of radioport architectures of radioports in a wireless communication network. The executable code instructs the processor to perform operations including specifying parameters associated with the radioports, the specifying operation specifying a constant channel capacity constraint, and computing composite powers for the radioport architectures in response to the parameters. Cost structures are determined in response to the composite powers for the radioport architectures, the cost structures being determined in response to the constant channel capacity constraint. The cost structures of the radioport architectures are compared to choose a least-cost one of the radioport architectures to be the one radioport architecture.  
           [0018]    The above and other advantages of the present invention are carried out in yet another form by a computer-based method for selecting one of a plurality of radioport architectures of radioports in a wireless communication network. The method calls for specifying parameters associated with the radioports, the specifying operation specifying a constant offered load constraint, and identifying sizes of coverage areas of the radioports. The method further calls for ascertaining a quantity of radioports to support wireless communication in a total service area of the wireless communication network in response to the sizes of the coverage areas. Composite powers are computed for the radioport architectures in response to the parameters and cost structures are determined in response to the composite powers for the radioport architectures, the cost structures being determined in response to the constant offered load constraint. The determining operation includes applying a cost model to determine costs of one of the radioports responsive to the sizes of the coverage areas and combining each of the costs with the quantity of the radioports to obtain the cost structures of each of the radioport architectures. The cost structures of the radioport architectures are compared to choose a least-cost one of the radioport architectures to be the one radioport architecture. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0019]    A more complete understanding of the present invention may be derived by referring to the detailed description and claims when considered in connection with the Figures, wherein like reference numbers refer to similar items throughout the Figures, and:  
         [0020]    [0020]FIG. 1 shows a diagram of a portion of a wireless communications network;  
         [0021]    [0021]FIG. 2 shows a graph of a cost curve associated with one of the radioports of the wireless network relative to a range of composite powers;  
         [0022]    [0022]FIG. 3 shows a graph of cost curves describing the relationship between composite powers and the total radio segment cost, C rad , for radioports using a quadratic cost model;  
         [0023]    [0023]FIG. 4 shows a graph of cost curves describing the relationship between composite powers and the total radio segment cost, C rad , for radioports using a linear cost model;  
         [0024]    [0024]FIG. 5 shows a flow chart of a constant channel capacity radioport modeling process in accordance with a first embodiment of the present invention;  
         [0025]    [0025]FIG. 6 shows a graph of cost curves describing a difference a constant offered load constraint has on the radio segment cost, C rad , for the quadratic cost model of FIG. 3;  
         [0026]    [0026]FIG. 7 shows a graph illustrating the total radio segment cost, C rad , at different blocking probability parameter values;  
         [0027]    [0027]FIG. 8 shows a graph of cost curves describing a difference the constant offered load constraint has on the radio segment cost, C rad , under the assumption of a different constant offered load then that of FIG. 6;  
         [0028]    [0028]FIG. 9 shows a flow chart of a constant offered load radioport modeling process; and  
         [0029]    [0029]FIG. 10 shows a graph of a cost curve describing the relationship between composite powers and the total radio segment cost generated in response to the modeling process of FIG. 9. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0030]    [0030]FIG. 1 shows a diagram of a portion of a wireless communications network  20 . Network  20  includes a plurality of radioports  22 , otherwise known as base stations, access points, base station transceivers, and so forth. Radioports  22  are radio transceivers, used to provide access for mobile users to a wireless communication network  20 . Radioports  22  provide radio communication service in their respective coverage areas  24 , also known as cells. Some of radioports  22  may include directional antennas, for subdividing their respective coverage areas  24  into sectors to more efficiently provide service in regions of dense user concentrations.  
         [0031]    The arrangement of wireless system cells has typically been modeled as a grid of adjoining hexagons (not shown). The hexagonal view is convenient for planning frequency reuse on a first order basis, but it is not well suited to describing actual wireless networks with cells that cover large geographical areas. This is primarily for two reasons. First, when large cells are used, geographical features (hills, valleys, bodies of water, etc.) dominate the propagation domain. Thus, cells must be located where they can achieve line-of-sight coverage to most of the desired coverage area. Second, cell sizes must vary widely to provide many cells per unit area in regions of dense user concentrations, as shown in a first region  26  in the upper right of network  20 , and fewer cells per unit area where user densities are lower, as shown in a second region  28  in the lower left of network  20 .  
         [0032]    This reflects the current state of practice in wireless engineering, which is to locate radioports  22  using educated guesses by inspecting maps of the intended service area. The differences between the hexagonal model used to define frequency reuse and the engineering practice used to locate radioports  22  mean that frequency reuse calculated from the hexagon model is generally quite different from that attained in practice. This has led to the development of complex computer models which exhaustively calculate signal levels at each radioport  22  from every other radioport, and assign frequencies based on the actual co-channel interference that is calculated.  
         [0033]    The problem faced by emerging technologies, such as personal communications service (PCS) and International Mobile Telecommunications for the year two thousand (IMT-2000) is somewhat different from that of traditional wireless systems. That is, in order to be profitable, these systems must serve large numbers of users in comparatively small geographical areas. In order to serve large numbers of users, these systems are being designed for significantly increased frequency reuse. Whereas the typical coverage radius of a cell site, or radioport, in an AMPS system is in the order of three to sixteen kilometers, PCS and other microcell services are planned for typical coverage radii of two to three kilometers or less. This means, of course, that it will take many more microcells to cover any given service area than it would take AMPS cells.  
         [0034]    It is anticipated that in user dense environments, such as first region  26  spatial dispersal of offered traffic load approaches a uniform distribution. Consequently, if radioport coverage radii are reduced such that traffic density is essentially uniform over a neighborhood of many adjacent sites, than appropriate radioport spacing will be uniform.  
         [0035]    If the coverage area layout is modeled by circles of common radii in the user dense environments, then those circular regions can be arranged in a regular geometric fashion. The circular model represents the coverage from some minimum signal strength.  
         [0036]    Implicit in this uniform cell arrangement may be an assumption that each radioport  22  in first region  26  provides the same traffic capacity or same number of transmission channels as do other radioports  22 . Under conditions of same traffic capacity each of radioports  22  will provide the same grade of service as do other radioports. This is a desirable condition for ubiquitous user mobility through a topology without significant degradation in service. For an initial system design, particularly with uniform spacing of radioports  22  as in first region  26  that is a reasonable assumption.  
         [0037]    Exceptionally high-density user clusters or propagation coverage voids that are known during the design phase of wireless network  20  can be covered by overlay radioports  22 . High-density user clusters or propagation voids which become known after a network is deployed may be dealt with in a number of ways, including overlay, all of which may be modeled and analyzed using known tools. Accounting for major differences in offered load across a geographic serving area may be dealt with by “banding” cell capacities in a model to correspond to load distribution. These approaches all serve to minimize any difference in grade of service observable by a user. Accordingly, uniform traffic capacity across radioports may be assumed.  
         [0038]    Based on the foregoing discussion, modeling the arrangement of radioports  22  as a uniform arrangement of circular cells of common radii is reasonable for networks serving dense user environments, such as in first region  26 . Therefore, the uniform cell arrangement will be used hereafter, as will an assumption of uniformly spatially-distributed traffic loading.  
         [0039]    The cost of each of radioports  22  depends on several things, but chief among these are channel capacity, power output, and physical construction. The interface circuitry between radioports  22  and the interconnecting infrastructure tends not to be sensitive to coverage radius. Thus, important cost drivers for radioports are the power that they must radiate and the physical construction requirements dictated by their placement. For example, a radioport that operates exposed to the weather will typically cost more than one designed to operate in a protected location, all other factors being equal. However, the protected radioport will incur the costs of a building location. Similarly, a radioport that operates at high power levels at low distortion will be more costly than one of lower power or higher distortion.  
         [0040]    The radioport composite power, P comp , of a radioport  22  is the total output power which its radio frequency (RF) power amplifier is capable of providing for some specified input at a stated distortion level. Radioport RF amplifiers are typically linear amplifiers. Therefore, the maximum composite power, P comp , is available only when the specified input is present.  
         [0041]    The power per channel, P ch , depends on the number of channels and the composite power. It is the power per channel, P ch , not the composite power output, P comp , that determines coverage area  24  of the radioport. The best case, i.e., the maximum coverage radius for a channel occurs when  
               P   ch     =       P   comp     N             (   2   )                               
 
         [0042]    where  
         [0043]    P ch  =power per channel  
         [0044]    P comp =maximum radioport composite power  
         [0045]    N=number of channels  
         [0046]    While the power per channel, P ch , can always be less than the value given by equation (2), for example, due to forward link power control, it cannot be greater than this value. The power per channel, P ch , cannot be greater because the maximum composite power output, P comp , from the linear amplifier is available only when the composite input power from N channels is present. Thus, equation (2) provides the upper bound on power per channel, P ch , which, in turn, determines the coverage radius, r, of the radioport.  
         [0047]    If sufficient data exist, it is possible to plot the cost of small radioports  22  (i.e., those smaller than typically used for cellular service) as a function of their composite power, P comp . FIG. 2 shows a graph  30  of cost curves  32  and  33  of exemplary costs  34  associated with one of radioports  22  (FIG. 1) of wireless network  20  (FIG. 1) relative to a range of composite powers, P comp ,  36 . Cost curves  32  and  33  are continuous curves in graph  30 . However, in reality composite powers, P comp ,  36  are discrete. That is, a 37.6-watt radioport is not purchased. Rather a thirty or fifty watt unit is purchased.  
         [0048]    As shown in graph  30 , the best fit to the data is a least-squares quadratic equation cost model with r 2 =0.7644 thus forming cost curve  32 . The least-squares quadratic equation cost model is as follows: 
           C   r =4.4095P comp   2 +263.04P comp +54435  (3) 
         [0049]    where, P comp =composite power of the radioport in watts (P comp  greater than or equal to 1 for this data set), and C r =cost of one radioport, measured in U.S. dollars. For this data set, a linear least-squares fit is nearly as good, with r 2 =0.7366, thus forming cost curve  33 . The linear equation cost model that best fits this data is given by: 
           C   r −676.07P comp   2 +50637.  (4) 
         [0050]    Equations (3) and (4) are valid only for this data set. Each wireless network should be evaluated based on the components available for its construction. While these values are satisfactory to develop models for testing, it will be demonstrated below that the cost function is the most sensitive element in determining the total radioport segment cost, C rad  (see equation (1)), and should be determined with accuracy for each network design.  
         [0051]    Small radioports are specified and purchased according to their composite power, but what is of interest in wireless network infrastructure design is their coverage and traffic-handling capacity. Coverage can be obtained from the per channel power, P ch , as defined in equation (2) after some additional parameters are defined, as discussed below.  
       Radioport Coverage Modeling: Constant Channel Capacity  
       [0052]    For networks where the radioport is well clear of surrounding obstacles, radioport coverage can be described by the known Hata representation of Okamura&#39;s propagation model, which is given by equation (5). This model is commonly used for wireless network propagation prediction. 
           L   p −69.55+26.16log 10   f− 13.82log 10   h   b   −A ( h   m )+(44.9−6.55log10 h   b )log 10   r   (5) 
         [0053]    where  
         [0054]    L p =path loss (in decibels)  
         [0055]    f=frequency (in MHz)  
         [0056]    r=distance from transmitter to receiver (coverage radius, in kilometers)  
         [0057]    h b =base station (radioport) antenna height (in meters)  
         [0058]    h m =mobile station antenna height (in meters)  
         [0059]    A(h m )=(1.1log 10 f-0.7) h m -(1.56log 10 f-0.9) for a small or medium city  
         [0060]    Hata&#39;s propagation model, as originally developed, is specified over the range 150≦f≦1500 MHz and 1≦d≦10 kilometers. Taken strictly in its original form, it would not be suitable for characterizing low power radioports with coverage radii less than a kilometer, nor for PCS services in the 1.8-2.2 GHz band. However, field measurements have shown that Hata&#39;s propagation model can be “tuned” by adjusting the constants to give quite accurate predictions for specific locales at frequencies at least as high as 3 GHz, and for distances somewhat less than 1 kilometer. Therefore, this model is used herein for propagation prediction.  
         [0061]    Although the Hata/Okamura propagation model is used herein, it should be apparent to those skilled in the art that other propagation prediction models may be used. The choice of another propagation model may lead to different specific results, but will not affect the general findings of this analysis.  
         [0062]    Path loss can be expressed in terms of both the required minimum received signal strength, P r , and the maximum transmitted power per channel, P ch , such that L p -P ch -P r , which enables equation (5) to be written in the form of equation (6): 
           r= 10α  (6) 
         [0063]    where  
             α   =     [         P   ch     -     P   r     -   69.55   -     26.16      log                 f     +     13.82      log                   h   b       +     a        (     h   m     )           44.9   -     6.55      log                   h   b           ]             (   7   )                               
 
         [0064]    The coverage model consists of an array of circular regions, each of radius r. Thus, the size of a coverage area, A cell , of any radioport can be expressed by utilizing Hata&#39;s propagation model in the form of equation (8). 
           A   cell   =πr   2 =π10 2α   (8) 
         [0065]    Wireless networks are designed to provide coverage over a known total service area, A tot . The number of cells, K, having radio coverage areas, A cell , required to cover this total service area, A tot  is given by K=A tot /A cell  subject to the constraint that each cell have the capacity to handle the same number of channels, as discussed previously. It follows that the total radioport segment cost of the radioports required for a wireless network covering A tot  is given by equation (9). 
           C   rad   =KC   r   (9) 
         [0066]    It is now possible to express the total radioport segment cost, C rad , to cover the total service area, A tot , in terms of the composite power, P comp , of an individual radioport, the number of channels, N, supported by the radioport, and the radioport unit cost, C r , by combining the results of equations (2), (8), and (9) to arrive at equation (10).  
               C   rad     =       C   r            A   iot       π10                β                   (   10   )                               
 
         [0067]    where:  
             β   =     [         20        log        (     P   ch     )         -     2        P   r       -   139.1   -     52.32      log                 f     +     27.64      log                   h   b       +     2        A        (     h   m     )             44.9   -     6.55      log                   h   b           ]             (   11   )                               
 
         [0068]    It is instructive to examine the nature of the fractional term that multiplies C r . Let  
               C   f     =       A   tot       π10   β               (   12   )                               
 
         [0069]    Then,  
                 ∂     C   f         ∂     P   ch         =     20          A   tot       π                       P   ch          (     44.9   -     6.55      log                   h   b         )       ·   10        β                 (   13   )                   ∂       C   2     f         ∂     P   ch   2         =       400          A   tot       π                         P   ch   2          (     44.9   -     6.55      log                   h   b         )       2     ·   10        β         +     20          A   tot       π                       P   ch   2          (     44.9   -     6.55      log                   h   b         )       ·   10        β                   (   14   )                               
 
         [0070]    For any real networks, A tot &gt;0, P ch &gt;0, h b ≧0, P r ≦0, f&gt;150, and A(h m )≧0. Furthermore, (44.9-6.55logh b )≦0 for h b ≦7.161×10 6  is also true. Under these constraints:  
                   ∂     C   f         ∂     P   ch         &gt;   0     ,         ∂     C   f         ∂     P   ch   2         &gt;   0             (   15   )                               
 
         [0071]    The conditions of equation (15) are sufficient to assert that, under the constraints described, equation (12) is convex on the range of P ch . Indeed, equation (12) is asymptotic to the axes in the first quadrant. It should be noted that the power per channel, P ch , is related to the minimum required received signal strength, P r , by a constant (i.e., equation (2)). So, it can be asserted that equation (12) is convex on P r . Equation (10) is therefore the product of a convex function and another function, C r . As such, the equation (10) is convex over the range of P r  for linear or convex C r , and possibly even for mildly concave C r . This implies that there exists a choice of radioport composite power, P comp , and number of radioports, K, that yields an optimal cost solution for the radioports required to cover the total service area, A tot . Both cost curves  32  and  33  describing the radioport costs in graph  30  (FIG. 2) are convex, so an optimal cost solution is readily apparent.  
         [0072]    Referring to FIGS.  3 - 4 , FIG. 3 shows a graph  38  of cost curves  40  describing the relationship between composite powers  36  and total radio segment costs, C rad ,  42  for radioports  22  (FIG. 1) using a quadratic cost model. In particular, graph  38  plots total radio segment costs  42  relative to composite powers  36  using the quadratic cost model of equation (3). FIG. 4 shows a graph  44  of cost curves  46  describing the relationship between composite powers  36  and the total radio segment cost, C rad ,  42  for radioports using a linear cost model. In particular, graph  44  plots total radio segment costs  42  relative to composite powers  36  using the linear cost model of equation (4). Each of cost curves  40  and  46  represents a different number of channels per radioport, ranging from five to twenty by an increment of five, assuming a total coverage area, A tot , of one hundred square kilometers.  
         [0073]    The functions plotted in each of graphs  38  and  44  of FIGS. 3 and 4 are strictly convex over their ranges, as they lie entirely below their chords. Graphs  38  and  44  have been plotted on the same scale, permitting 1:1 comparison. It should be noted that the choice of model for radioport costs matters significantly to both the choice of composite power, P comp , and to the resultant radioport segment cost, C rad . Indeed, had the linear and quadratic expressions of this data set differed more than they do, the differences would have been more marked.  
         [0074]    It is worth noting that, had one chosen to model the cost data by a logarithmic function cost model (which has a low coefficient of correlation, but which is a concave function), the plot of total radio segment cost  42  versus composite power  36  is still convex, although not as strongly so. This suggests that under most conditions for realistic systems with radioports of like channel capacity, an analytically determinable cost optimal solution exists for the radioport segment cost.  
         [0075]    [0075]FIG. 5 shows a flow chart of a constant channel capacity radioport modeling process  48  in accordance with a first embodiment of the present invention. Process  48  is performed to select one of a plurality of radioport architectures of radioports  22  (FIG. 1) for first region  26  (FIG. 1) of wireless communications network  20  (FIG. 1). A radioport architecture provides definition for the number of radioports  22  needed to provide service to a total service area, A tot , the radioport coverage areas, A cell , the power per transmission channel, P ch , and the number of transmission channels, N, needed per radioport.  
         [0076]    The object of process  48  is to find a least-cost radioport architecture under the conditions of a constant channel capacity constraint. That is, process  48  is subject to the constraint that each of radioports  22  (FIG. 1) in first region  26  have the capacity to handle the same number of transmission channels, as discussed above.  
         [0077]    Process  48  may be in the form of executable code contained on a computer-readable storage medium (not shown) which is executable using standard desktop engineering tools and processors. The computer-readable storage medium may include a hard disk drive internal or external to a processor, a magnetic disk, compact disk, or any other volatile or non-volatile mass storage system readable by a processor. The computer-readable storage medium may also include cooperating or interconnected computer readable media, which exist exclusively on a computing system (not shown) or are distributed among multiple interconnected computer systems (not shown) that may be local or remote.  
         [0078]    Constant channels radioport modeling process  48  begins with a task  50 . At task  50 , parameters associated with radioports  22  are specified. Under constant channel capacity constraints, the parameters specified at task  50  include mobile station antenna height (in meters), h m ; required minimum received signal strength, P r ; frequency (in MHz), f; base station (radioport) antenna height (in meters), h b ; and total service area, A tot . For clarity of illustration, the following parameters are specified at task  50 ; h m =2, P r =−92 dBm, f=2000, h b =10, A tot =100. In addition, a counting variable, t, is set as t=1, 2 . . . 400.  
         [0079]    Following task  50 , a task  52  is performed. At task  52 , a number of transmission channels, N, is defined. In the illustrative example, the number of transmission channels is defined in increments of five, that is, N=5, 10, 15, 20. However, as discussed previously the number of transmission channels, N, is held constant for each of radioports  22  in the total service area, A tot , for a given radioport architecture.  
         [0080]    A task  54  is performed in response to task  52 . At task  54 , a power per channel, P ch , is established. In an exemplary embodiment power per channel, P ch , is established using the following function, P ch =0.1t, where t is the counting variable specified in task  50 . Hence, at task  54 , the power per channel, P ch =0.1 Watts.  
         [0081]    Following task  54 , a task  56  identifies radioport coverage area, A cell . As discussed previously, the size of the coverage area of any cell, A cell , can be expressed by utilizing Hata&#39;s propagation model in the form of equation (8). Furthermore, as shown in equation (7), the coverage area of any cell, A cell , depends in part upon the power per channel, P ch . Hence, in the execution of task  56 , a large value of power per channel, P ch  will yield a larger coverage area, A cell , than a smaller value of P ch , all other variables being held constant.  
         [0082]    Following task  56 , a task  58  computes radioport composite power, P comp , using equation (2) for each of the N transmission channels defined in task  52  and the power per transmission channel, P ch .That is, P comp -NP ch  is computed for each of N=5, N=10, N=15, and N=20.  
         [0083]    In response to task  58 , a task  60  is performed to compute a number of cells, hence the quantity, Q, of radioports  22  needed to provide service in total service area, A tot , given the identified sizes of radioport coverage areas, A cell . The quantity of radioports  22  is computed under the realization that Q=A tot /A cell .  
         [0084]    A task  62  is performed in connection with task  60 . At task  62 , the total radioport segment cost, C rad , is computed by employing equation (9). In the exemplary illustration the cost of one radioport, C r , is modeled by applying the linear fit cost model of equation (4). Hence, C rad  at counting variable t, and N transmission channels is represented by:  
                 C   rad          (     t   ,   N     )       =         A   tot       A   cell            (     50637   +     (     676.09      N                   P   ch       )                       =       A   tot     ·       [     50637   +     (     676.09        NP   ch       )       ]       π10     (         2                 10        log        (     P   ch     )         -     2   ·     P   ch       -     139                 1     -     5232   ·     log        (   f   )         +     27                   64   ·     log        (     h   b     )           +     2   ·     A   cell           44.9   -     6.55   ·     log        (     h   b     )             )                                       
 
         [0085]    Thus at task  62 , the total radioport segment cost, C rad , is computed for each of N=5, N=10, N=15, and N=20 channels allocated to each of radioports  22 .  
         [0086]    Following task  62 , a query task  64  determines if process  48  is complete. In this exemplary illustration, process  48  is done when the counting variable, t, is equivalent to its predetermined maximum. In this case, the predetermined maximum of t, specified at task 50, is 400. Thus, when query task  64  determines that the counting variable, t, is less than or equal to 400, process  48  is not complete, and program control proceeds to a task  66 .  
         [0087]    At task  66 , a next power per channel, P ch , is established by incrementing the counting variable, t, and recomputing, P ch =0.1t.  
         [0088]    Following task  66 , program control loops back to task  56  to compute the radio coverage area, A cell , in view of the next power per channel, P ch , and to ultimately compute the total radio segment cost, C rad , given the incremented power per channel, P ch . As such, under the condition of a constant channel capacity constraint, process  48  iteratively varies the channel transmission powers, or power per channel, P ch , and calculates composite powers, P comp , in response to the defined number of transmission channels, N, and the varying channel transmission powers.  
         [0089]    When query task  64  determines that process  48  is done, that is, the counting variable, t, exceeds the predetermined maximum of 400, process  48  proceeds to a task  68 .  
         [0090]    At task  68 , cost structures, in the form of cost curves, are plotted for each of the N=5, N=10, N=15, and N=20 transmission channels. Referring to FIG. 4 in connection with task  68 , graph  44  shows cost curves  46  for each of the N=5, N=10, N=15, and N=20 transmission channels plotted at task  68 . As discussed previously, the cost structures illustrated by cost curves  46  describe the relationship between composite powers  36  and the total radio segment cost, C rad ,  42  for radioports using the linear cost model of equation (4).  
         [0091]    A task  69  is performed in connection with task  68 . At task  69 , a least-cost one of the radioport architectures is selected. With continued reference to graph  44  of FIG. 4, since cost curves  46  are convex, an analytically determinable cost optimum solution exists for the radioport access segment, at the point along each of cost curves  46  where total radioport segment costs, C rad ,  42  are at a minimum.  
         [0092]    At this minimum total radioport segment cost, C rad , for a particular number of transmission channels, N, the minimum composite power, P comp , is readily ascertained. From this minimal composite power, P comp , the cost optimal quantity of radioports having radio coverage areas, A cell , for supporting wireless communication in the total service area, A tot , of wireless network  20  (FIG. 1) and power per channel, P ch , values associated with the composite power, P comp  are specified to reveal the least-cost radioport architecture responsive to a constant channels capacity constraint. Following task  69 , process  48  exits.  
       Radioport Coverage Modeling: Constant Offered Load  
       [0093]    As discussed previously, an economically optimum solution for radioport size (i.e., coverage area, A cell ) was found under conditions of equal channel capacity at all radioports  22  (FIG. 1) as illustrated through the execution of constant channels radioport modeling process  48  (FIG. 5). The problem of determining an economically optimum solution for radioport size is now considered from the viewpoint of the offered call traffic load. For purposes of this discussion, it is assumed that the offered load, expressed in Erlangs per unit area, is constant over the geographic area of concern.  
         [0094]    Reasonable assumptions in the design of wireless network infrastructure includes infinite traffic sources, equal traffic density per source, and that lost calls are cleared. The Erlang B equation presumes these assumptions and is commonly used to design wireless communications networks. The Erlang B equation is given by:  
               P   b     =         E   N       N   !           ∑     k   =   0     N            E   k       k   !                   (   16   )                               
 
         [0095]    where:  
         [0096]    P b =blocking probability  
         [0097]    E=offered load in Erlangs for a unit area at busy hour  
         [0098]    N=number of channels (in the serving cell)  
         [0099]    Practical networks seek to hold the value of the blocking probability, P b , as constant as possible across the network, so that users experience the same blocking probability, P b , wherever they are. Thus, P b  is held constant in this discussion. The blocking probability, P b , is a quality of service parameter. That is, a lower blocking probability, P b , yields higher quality of service because fewer calls may be blocked as compared to a higher blocking probability, P b , which may result in more calls that may be blocked.  
         [0100]    Examining the denominator of equation (16), it is seen that:  
                 lim     N   →   ∞              ∑     k   =   0     N            E   k       k   !           =       1   +   E   +       E   2       2   !       +       E   3       3   !       +   …                =     e   E               (   17   )                               
 
         [0101]    Therefore, it is asserted that for a large number of channels, N,  
                 ∑     k   =   0     N            E   k       k   !         ≅        E             (   18   )                               
 
         [0102]    This allows the expression of equation (16) to be written as an exponential approximation as follows:  
                 P   b             E       ≅       E   N       N   !               (   19   )                               
 
         [0103]    Equation (19) would usually be solved with N and E as the independent variables to produce the values of the blocking probability, P b , which can take any positive value. In this scenario, the blocking probability, P b , becomes the independent variable. Software exists that evaluates this equation as stated to find N by iteration, and solutions can usually be found. However, many of these solutions will be erroneous. In mathematical terms, it is not possible to compute the factorial of a non-integer. In physical terms, it is impossible to allocate a fractional channel. Thus, only integer values of N have any meaning. To deal with this problem, the approach taken herein is to compute the roots of equation (19) by determining when the residual changes from negative to positive, varying N by integral increments.  
         [0104]    Equation (19) can, under some circumstances (e.g., large offered load, E), have two roots. The most positive root of equation (19) for any given values of P b  and E will be denoted N pb,E  and is the root sought. It is possible to construct a family of curves for various values of blocking probability, P b , and offered traffic, E, which indicate values for the number of channels, N, under those circumstances. As it turns out, N is not particularly large for small coverage areas and low traffic loads. However, as long as N≧2, which will always be the case, the approximation of equation (18) is within eight percent, with the accuracy improving as N increases. Thus, the approximation of equation (18) is sufficiently accurate for the purposes of this analysis given that channels are discrete.  
         [0105]    The difference between the constant allocated channel and constant offered load models is not trivial. Under the constraints of equation (10), as cells diminish in size the quality of service improves (i.e., the blocking probability decreases) because the same number of channels are allocated to cover a smaller geographical area as were available to cover a larger area. Under the constraints of equation (19), however, the blocking probability remains constant, and the number of channels is allowed to change according to the area, A cell , to be covered, which in turn affects the composite power required of the radioport.  
         [0106]    [0106]FIG. 6 shows a graph  70  of cost curves  72  describing a difference the constant offered load model has on the total radio segment cost, C rad ,  42  relative to composite powers, P comp ,  36  for the quadratic cost model of FIG. 3. The essential difference between the constant channel capacity approach and the constant offered load approach is that the results described in graph  70  are not the representation of a continuous function. Indeed, the comparison of graph  38  (FIG. 3) and graph  70  reveals several important similarities and differences between the approaches of providing a constant number of channels and providing a constant offered load, that is, a constant quality of service.  
         [0107]    First, the curves plotted in graph  70 , although not the representation of strictly continuous functions, appear to meet the essential characteristics of convex functions, as did the curves plotted in graph  38  (FIG. 3). It is generally possible to construct a chord between any two points on the curve below which lies the remainder of the curve, thus indicating the presence of a single global minimum. Because these are not the curves of a continuous function, mathematically it is not possible to prove their convexity directly, but inspection of graph  70  provides a strong case that they are essentially so. Were a mathematical proof of convexity to be required, it is obvious by inspection of graph  70  that the data of any of the curves could be fitted closely to a parabola. As the first derivative of a parabola is strictly increasing and the second derivative is positive, it is strictly convex.  
         [0108]    Second, the comparison of graph  38  (FIG. 3) and graph  70  indicates that the minimum cost point under the constraint of constant offered load occurs at a lower composite radioport power, P comp . Minimum cost occurs with radioports of approximately 63 watts for a ten percent blocking probability, P b , (represented by squares) and 29.5 watts for a two percent blocking probability, P b , (represented by triangles) in the 0.1 Erlangs/km 2  constant load situation. As shown in graph  38  (FIG. 3), in the case of constant offered channels, the minimum composite power, P comp , for minimum cost for the same number of channels is 354 watts.  
         [0109]    This outcome is not totally unexpected, but its magnitude graphically illustrates a major benefit of small radioports serving small radio coverage areas, A cell . Small radioports require much less in the way of site space and electrical mains power, and present less environmental impact. These properties contribute profoundly to reducing the site costs for small radioports as compared to larger versions.  
         [0110]    Third, the total radioport segment cost, C rad , under the case of constant offered load is substantially lower than for the constant offered channel design. For the case of a two percent blocking probability, P b , at 0.1 Erlangs/km2 constant offered load, total radio segment cost, C rad , shown in graph  70  is approximately $1.2 million. This is compared to a total radio segment cost, C rad , shown in graph  38  (FIG. 3) of $196.2 million in the equivalent situation of constant offered channels, or a ratio of over 160 to 1 in favor of providing constant offered load, i.e., a constant quality of service. Hence, the variance between the two approaches is striking.  
         [0111]    [0111]FIG. 7 shows a graph  74  illustrating the total radio segment cost, C rad ,  42  at different blocking probability parameter, P b  values  76 . Graph  74  shows that the total radio segment cost  42  of providing an excellent blocking probability, P b , of one half percent are only approximately twenty percent higher than providing a poor blocking probability of ten percent for the example of graph  70  (FIG. 6). Graph  74  shows an even more noteworthy outcome. The total radioport segment cost, C rad ,  42  is approximately equivalent for blocking probabilities of ten to five percent and for blocking probabilities from one percent to one half percent. Accordingly, it costs nothing additional to reduce the blocking probability, P b , from ten percent to five percent or from one percent to one half percent. The reason for this outcome is that channels must be assigned discretely. That is, one cannot assign a fraction of a channel. Because radio coverage areas, A cell , are small in this case, relatively low numbers of channels, N, are required, and adding or deleting a single channel per cell has a large affect on the blocking probability, P b .  
         [0112]    The impact of this finding on network design is significant. It is possible to quantify the economics of improved blocking probability, P b  (i.e., higher quality of service), at the initial network design stage. This enables the network to be designed and installed initially with the most likely quality of service in place, at little to no added cost compared to the conventional minimalist approach. Thus, the initial design of wireless communications network  20  (FIG. 1) will have better quality of service than networks designed using more traditional approaches. This, in turn, should lead to higher customer take rates and lower customer churn. It should also preclude the necessity to augment or expand the network for a considerable period, which reduces operating and investment costs. These factors are not readily modeled, but they are critical marketplace realities.  
         [0113]    [0113]FIG. 8 shows a graph  78  of cost curves  80  describing a difference the constant offered load model has on the radio segment cost, C rad ,  42  under the assumption of a different constant offered load then that of graph  70  of FIG. 6. In particular, cost curves  80  are plotted in graph  78  for the same quadratic cost model and one hundred square kilometer coverage area, A tot , that was used in FIG. 6, under the assumption of a constant offered load of 1 Erlangs/km 2 . Graph  78  confirms that the results depicted in FIG. 6 are not unique. That is, it can be seen in graph  78 , that cost curves  80 , although not strictly convex over their defined range have clear global minima which can be exploited in the design of wireless communications network  20  (FIG. 1).  
         [0114]    Graph  78  shows that no added investment is needed to achieve an order of magnitude increase in the grade of service, i.e. the increased offered load of 1.0 Erlangs/km 2 . Accordingly, the total radioport segment cost, C rad , under these conditions is not strongly sensitive to the offered load per unit area. The cost curves shown in FIGS. 6 and 8 show that the high cost and uncertainty of comprehensive marketing studies can be avoided in favor of much less expensive surveys and experimental data in designing network  20 .  
         [0115]    [0115]FIG. 9 shows a flow chart of a constant offered load radioport coverage modeling process  82  in accordance with a second embodiment of the present invention. Like process  48  (FIG. 5), process  82  is performed to select one of a plurality of radioport architectures of radioports  22  (FIG. 1) for first region  26  (FIG. 1) of wireless communications network  20  (FIG. 1). As discussed previously, a radioport architecture provides definition for the number of radioports  22  needed to provide service to a total service area, A tot , the radioport coverage areas, A cell , the power per transmission channel, P ch , and the number of transmission channels, N, needed per radioport.  
         [0116]    The object of process  82  is to find a least-cost radioport architecture under the conditions of a constant offered load constraint. That is, process  82  is subject to the constraint that each of radioports  22  (FIG. 1) manages the same, or a constant, offered call traffic load in first region  26  as discussed above. As discussed in connection with process  48  (FIG. 5), process  82  may be in the form of executable code contained on a computer-readable storage medium (not shown) which is executable using standard desktop engineering tools and processors.  
         [0117]    Constant offered load radioport modeling process  82  begins with a task  84 . At task  84 , parameters associated with radioports  22  are specified. Like process  48 , the parameters specified at task  84  include mobile station antenna height (in meters), h b ; required minimum received signal strength, P r ; frequency (in MHz), f; base station (radioport) antenna height (in meters), h b ; and total service area, A tot . In addition, under the constant offered load constraints, the distance from transmitter to receiver (coverage radius, in kilometers), r; the offered load in Erlangs per unit area, E, and a blocking probability, P b , are also specified at task  84 . By way of illustration, at task  84  the following parameters are specified h m =2, P r =−92 dBm, f=2000, h b =10, A tot =100, ε=1 Erlangs/km 2 , P b =0.01. In addition, radius, r, is specified using the following function, r=0.25+0.01t, where t is a counting variable, specified as t=1, 2, . . . 45. During a first iteration of process  82 , t=1, therefore radius, r, is 0.26 km.  
         [0118]    Following task  84 , a task  86  identifies the radioport coverage area, A cell . Each of the radioport coverage areas, A cell , of radioports  22  (FIG. 1) are defined to be circular regions of common radii, namely radius r. Accordingly the radioport coverage area, A cell , are readily computed using equation (8) for the specified radius, r.  
         [0119]    In response to task  86 , a task  88  determines the power per channel, P ch , for the specified radius, r, by applying the Hata propagation model of equations (6) and (7).  
         [0120]    Next, a task  90  computes an offered load, E, for each of the radio coverage areas, A cell . The offered load, E, is the total load offered in the radio coverage area, A cell . Under the constant offered load constraint, each of radio coverage areas, A cell , receives the same offered load. As such the offered load, E, can be computed by the following equation, E=εA cell . Following task  90 , a task  92  determines the number of transmission channels, N, needed to serve the offered load, E, computed at ask  90 . The exponential approximation to the Erlang B equation represented by equation (19) is used as follows:  
                   P   b             E       =       A   N     /     N   !         ,       expressed                 as                 F     =     G        (   N   )                            N        (   t   )       :=                j   ←                                                                                                                                1                 if                 t     &lt;   6                                (     t   -   5     )                   otherwise                   while                     P   b     ·        E         &lt;         (   E   )     j       j   !                   j   ←     j   +   1               j                   N   t     :=     N        (   t   )                             
 
         [0121]    Following task  92 , a task  94  is performed. At task  94 , radioport composite power, P comp , is computed. Since power per channel, P ch , was determined at task  88  and the number of transmission channels, N, was determined at task  92 , radioport composite power, P comp , is readily computed by employing equation (2).  
         [0122]    In response to task  94 , a task  96  computes a quantity, Q, of radioports  22  (FIG. 1) needed to provide service in total service area, A tot . Since radio coverage areas, A cell , are the same for each of radioports  22 , the quantity, Q, is readily computed as Q=A tot /A cell .  
         [0123]    A task  98  follows task  96 . At task  98 , the total radioport segment cost, C rad , is computed. That is, since the quantity, Q, of radioports computed at task  96  is known, equation (9), and the linear cost model of equation (4) for one of the radioports (4) are combined to compute the total radio segment cost, C rad , for the specified radius, r, as C rad =Q(50637+676.09P comp ).  
         [0124]    Following task  98 , a query task  100  determines if process  82  is complete. In this exemplary illustration, process  82  is done when the counting variable, t, is equivalent to its predetermined maximum. In this case, the predetermined maximum of t, specified at task  84 , is  45 . Thus, when query task  100  determines that the counting variable, t, is less than or equal to  45 , process  82  is not complete, and program control proceeds to a task  102 .  
         [0125]    At task  102 , the radius, r, is increased by incrementing the counting variable, t, and recomputing, r=0.25+0.01t.  
         [0126]    Following task  102 , program control loops back to task  86  to compute the radio coverage area, A cell , in view of the next radius, and to ultimately compute the total radioport segment cost, C rad , given the incremented radius, r.  
         [0127]    When query task  100  determines that process  82  is complete, that is, the counting variable, t, exceeds the predetermined maximum of 45, process  82  proceeds to a task  104 .  
         [0128]    At task  104 , a cost curve is plotted relating total radioport segment costs, C rad , with composite power, P comp , computed under a constant offered load constraint and in view of a particular blocking probability, P b .  
         [0129]    Referring to FIG. 10 in connection with task  104 , FIG. 10 shows a graph  106  of a cost curve  106  describing the relationship between composite powers  36  and total radio segment cost, C rad ,  42  generated in response to task  104  of constant offered traffic radioport modeling process  82  (FIG. 9).  
         [0130]    With continued reference to FIGS. 9 and 10, a task  105  is performed in connection with task  104 . At task  105 , a least-cost one of the radioport architectures is selected. Like graph  44  (FIG. 4) since cost curve  106  is convex, an analytically determinable cost optimum solution exists for the radioport access segment, at the point along cost curve  106  where total radioport segment cost, C rad ,  42  is at a minimum. As shown in graph  106 , a least cost solution can be readily visualized at radioport composite power, P comp , of approximately ninety watts. From this minimal composite power, P comp , the cost optimal quantity of radioports having radio coverage areas, A cell , for supporting wireless communication in the total service area, A tot , of wireless network  20  (FIG. 1) and power per channel, P ch , values associated with the composite power, P comp , and the defined number of channels, N, are specified to reveal the least-cost radioport architecture responsive to a constant offered load constraint. Following task  105 , process  82  exits.  
         [0131]    It should be understood that nothing in the development of the constant offered load model described in connection with process  82  (FIG. 9) constrains its use to a simple closed surface. The model is equally applicable to coverage areas such as an annulus. Thus, faced with a load model in which the offered load is exponentially decreasing for a distance away from a center point the becoming uniform, one could model annular bands of approximately commensurate offered load, and use the models discussed above to ascertain an economical disposition and coverage area of radioports in that situation. In addition, it is not necessary to segment the offered load too finely, which further decreases the complexity and cost of designing wireless network  20 .  
         [0132]    The total radioport segment cost, C rad , in wireless networks has historically included more than merely the radio equipment. A significant cost element in first-generation cellular systems is the cost of facilities. This includes land, buildings, towers, antennas, utility construction (e.g., electrical power line), backup power equipment, permits, maintenance, and insurance. These costs are often insensitive to the coverage radius, r, of the radioport, at least over reasonable ranges of coverage. However, it is clear that a forty watt radioport that can be mounted on a utility pole will require less facility cost investment than a one thousand watt rural cellsite that must be located in a building with environmental controls, security, and a large antenna and tower.  
         [0133]    Small radioports are not devoid of facilities costs. Mounting a radioport on a utility pole or a building has a cost, as does feeding power to it. Typically, these costs are less than for first-generation wireless networks, because the radio equipment itself is smaller, lighter, and less demanding of space and power for its operation. On the other hand, there are more of them than of first-generation cellsites. The facilities cost cannot be ignored.  
         [0134]    Facilities costs can be modeled as an additive term to the radioport cost function. If the costs are sensitive to the cell radius, r, or to the number of channels, N, that dependency should be included in the model. However, this is seldom the case. In general, this additive term is nearly constant over the range of parameters being considered. The effect of adding a constant to a convex function is merely to shift the function&#39;s ordinate values, not to alter its characteristics. Therefore, the modeling described herein can be used in the general case, with suitable customization for the specifics of the wireless network being designed.  
         [0135]    In summary, the present invention teaches of a method for modeling radioports in dense user environments. A total radioport segment cost element, C rad , has been shown to be convex so that an optimal cost solution exists. Furthermore, under the constraints identified herein, it has been found that a cost optimal solution may be found analytically rather than heuristically. Accordingly, options for radioport coverage areas may be considered by evaluating the number of channels, N, the composite power, P comp , the offered load, and the desired quality of service, selecting the least-cost solution, and applying it to a wireless communication network.  
         [0136]    It should be understood that it has been shown that in general, the route to a lower cost infrastructure does not lie in conventional approaches such as simply minimizing the number of radioports in a network, but rather requires a more thorough examination of interacting factors which drive network cost.  
         [0137]    Although the preferred embodiments of the invention have been illustrated and described in detail, it will be readily apparent to those skilled in the art that various modifications may be made therein without departing from the spirit of the invention or from the scope of the appended claims. For example, those skilled in the art will appreciate that the present invention will accommodate a wide variation in the specific tasks and the specific task ordering used to accomplish the processes described herein.