Abstract:
Technologies are provided herein for modifying mobile network signal propagation predictions. According to embodiments, signal characteristics are received from a network management system. The signal characteristics correspond to signals propagating in a predetermined portion of a mobile telephone network. An initial signal propagation prediction that corresponds to the predetermined portion of the mobile telephone network is also received. The initial signal propagation prediction is modified based on the received signal characteristics to produce a more accurate signal propagation prediction.

Description:
BACKGROUND 
       [0001]    A wireless telephone signal experiences path loss as it propagates from a mobile telephone to a mobile network transceiver. Path loss (also called path attenuation) is the reduction in the power of an electromagnetic wave as it travels from one location to another. Path loss may be due to many effects, such as, for example, a signal being partially absorbed or deflected by trees and buildings along the signal path. Path loss is influenced by terrain contours, environment (e.g., urban vs. rural), propagation medium (dry vs. moist air), the distance between a transmitter and a receiver, and the height and location of antennas. 
         [0002]    Propagation predictions are commonly used in radio network planning and optimization tools. In order to improve prediction accuracy, most propagation models have internal parameters that can be used to fine tune predictions to account for specific propagation conditions over a certain area. Test data is traditionally used to fine-tune propagation models based on a comparison of predicted versus measured signal strength for each location. Optimum propagation model parameters can be derived that minimize the error of the predicted signal strengths. The main disadvantage of this approach, however, is the need for extensive drive testing, which is very time-consuming and not scalable. 
         [0003]    It is with respect to these considerations and others that the disclosure presented herein has been made. 
       SUMMARY 
       [0004]    Technologies are provided herein for modifying mobile network signal propagation predictions. According to embodiments, signal characteristics are received from a network management system. The signal characteristics correspond to signals propagating in a predetermined portion of a mobile telephone network. Examples of the signal characteristics include values for received signal strength indicators, signal timing advance, and a signal interference matrix. 
         [0005]    An initial signal propagation prediction that corresponds to the predetermined portion of the mobile telephone network is also received. The initial signal propagation prediction is modified based on the received signal characteristics to produce a more accurate signal propagation prediction. The initial signal propagation prediction may also be modified based on estimated signal characteristics corresponding to the predetermined portion of the mobile telephone network. 
         [0006]    It should be appreciated that the above-described subject matter may also be implemented as a computer-controlled apparatus, a computer process, a computing system, or as an article of manufacture such as a computer-readable medium. These and various other features will be apparent from a reading of the following Detailed Description and a review of the associated drawings. 
         [0007]    This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended that this Summary be used to limit the scope of the claimed subject matter. Furthermore, the claimed subject matter is not limited to implementations that solve any or all disadvantages noted in any part of this disclosure. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0008]      FIG. 1A  is a block diagram illustrating a communication system, according to exemplary embodiments; 
           [0009]      FIG. 1B  is a block diagram illustrating a scaling system for propagation prediction scaling in one embodiment; 
           [0010]      FIG. 2  is a schematic diagram illustrating a traffic map sector, according to exemplary embodiments; 
           [0011]      FIG. 3  is a block diagram illustrating an example of calculating an interference matrix error metric applicable to individual sectors in one embodiment; 
           [0012]      FIG. 4  is a flow diagram illustrating an example of global error calculation, according to exemplary embodiments; 
           [0013]      FIG. 5  is a table illustrating a solution area used to determine a correction factor, according to exemplary embodiments; 
           [0014]      FIG. 6  is a table illustrating an iterative method for determining optimum correction factors for the solution area shown in  FIG. 5 , according to exemplary embodiments; 
           [0015]      FIG. 7  is a flow chart illustrating a method for scaling predictions for signal propagation, in accordance with exemplary embodiments; 
           [0016]      FIG. 8  is a flow chart illustrating a method for determining optimum correction factors; 
           [0017]      FIG. 9  is a block diagram illustrating a computer capable of implementing aspects of the technologies presented herein, in accordance with exemplary embodiments; 
           [0018]      FIG. 10  illustrates a pixel scaling process for best server RSSI and one of the interferers in one embodiment; and 
           [0019]      FIG. 11  shows a comparison of OSS C/I statistics vs. predicted C/I before and after pixel scaling is depicted according to one embodiment. 
       
    
    
     DETAILED DESCRIPTION 
       [0020]    The following detailed description is directed to technologies for modifying mobile network signal propagation predictions. In the following detailed description, references are made to the accompanying drawings that form a part hereof, and which are shown by way of exemplary embodiments and implementations. 
         [0021]    Note that although the subject matter presented herein has been described in conjunction with one or more particular embodiments and implementations, it is to be understood that the embodiments are not necessarily limited to the specific structure, configuration, or functionality described herein. Rather, the specific structure, configuration, and functionality described herein are disclosed as examples. Various modifications and changes may be made to the subject matter described herein without following the exemplary embodiments and applications illustrated and described, and without departing from the true spirit and scope of the embodiments. 
         [0022]    Referring now to the FIGURES, technologies for modifying mobile network signal propagation predictions will be described. Path loss normally includes propagation losses such as, for example, losses due to absorption and diffraction of the electromagnetic waves. Furthermore, a signal radiated by a transmitter may travel along many and different paths to a receiver. This propagation of a signal is called multipath. Multipath can either increase or decrease received signal strength, depending on whether the individual multipath wave fronts interfere constructively or destructively. The total power of interfering waves may vary quickly as a function of location resulting in fast fades which are very sensitive to receiver position. 
         [0023]    Path loss is usually expressed in dB. In its simplest form, the path loss can be calculated using the formula L= 10  n log 10  (d)+C, where L is the path loss in decibels, n is the path loss exponent, d is the distance between the transmitter and the receiver (usually measured in meters), and C is a constant which accounts for system losses. Calculation of the path loss is usually called propagation prediction. Exact propagation predictions are possible only for simple cases. For practical cases the propagation predications are calculated using a variety of methods. Among the most commonly used methods for propagation predictions are COST-231, Okumura-Hata, and W.C.Y.Lee. 
         [0024]    Propagation models having optimized model parameters can be used to provide more accurate signal strength predictions. Radio measurement information reported by mobile network stations can be used for propagation model tuning. For example, measurement reports are received and processed by a mobile network, which computes a set of radio statistics that are made available for optimization and trouble-shooting purposes in general. Using processed statistics from a network management system (NMS) instead of test measurements substantially reduces the amount of data to be managed and reduces or eliminates the need for special features or probes for collecting mobile network test measurement data and for manual data collection (e.g., drive tests). 
         [0025]      FIG. 1A  is a block diagram illustrating a communication system  109 , according to exemplary embodiments. The communication system  109  includes a network management system (NMS)  106  and a scaling system  100 . The NMS  106  is a tool for monitoring and managing the mobile telephone network  107 . The NMS  106  provides the scaling system  100  with signal characteristics  108  corresponding to mobile telephone communications within the mobile telephone network  107 . The signal characteristics  108  may include, for example, values for received signal strength indicators, signal timing advance, and/or a signal interference matrix. An interference matrix includes rows and columns of values that indicate interference between mobile phones or mobile phone sectors. A timing advance value is based on a length of time that a signal takes to travel between a mobile phone and a base station. A timing advance distribution per sector includes timing advance values for various sectors or portions of sectors. 
         [0026]    The scaling system  100  uses the signal characteristics  108  to revise signal propagation predications for the mobile telephone network  107 . For example, the scaling system  100  may compare the signal characteristics  108  with corresponding estimated signal characteristics to determine one or more error factors. Correction factors for scaling propagation predictions may then be determined based on the error factors. For example, correction factors corresponding to a minimum error factor may be selected. Optimum correction factors per sector can be determined using an iterative algorithm. For example, after changing predictions for each sector, the dominance areas, prediction statistics, and prediction correction factors can be re-calculated. 
         [0027]    According to exemplary embodiments, signal propagation predictions for respective locations within the mobile telephone network are corrected based on one or more correction factors that account for the distance between a mobile telephone and a corresponding base station, the macro-cell propagation model to be optimized, and the clutter type of the location. These correction factors, also referred to herein as path loss correction factors, can be expressed in mathematical terms. Path loss correction factors can be determined for each sector so that an error term corresponding to predicted vs. measured radio performance metrics is minimized. 
         [0028]      FIG. 1B  is a block diagram illustrating a scaling system  100  for propagation prediction scaling. The scaling system  100  includes a prediction scaling module  101 , a prediction statistics module  102 , an error measurement module  103 , and a prediction correction factor module  104 . The prediction scaling module  101  computes new scaled predictions based on correction factors received from the prediction correction factor module  104  and on original propagation predictions. According to exemplary embodiments, the prediction scaling module  101  uses the following formula: scaled predictions (azimuth, distance)=original predictions (azimuth, distance)+K 1 +K 2 *log 10  (distance), where K 1  and K 2  are correction factors that can have positive or negative values. K 1  is a correction for intercept distance attenuation and K 2  is a correction prediction attenuation slope with distance. Alternative propagation scaling formulas can also be utilized in other embodiments. 
         [0029]    The prediction statistics module  102  computes estimates for received signal strength indicator (RSSI) levels, an interference matrix (IM), and time advance (TA) values based on the scaled predictions from the prediction scaling module  101  and on a traffic map. A traffic map identifies the concentration or intensity of mobile phone signals in corresponding geographical areas. The traffic map received by the prediction statistics module  102  may be an actual traffic map or an estimated traffic map. An optional traffic map derivation module  105  may be used to provide an estimated traffic map to the prediction statistics module  102 . The predication statistics module provides the estimates for RSSI, IM, and TA values to the error measurement module  103 . 
         [0030]    The error measurement module  103  computes an error metric based on a comparison of estimates for RSSI, IM and TA values with corresponding values received from the NMS. An example of IM error metric applicable to individual sectors is illustrated in  FIG. 3 . The error measurement module  103  provides the error metric to the prediction correction factor module  104  which uses the error metric to select new KI and K 2  values. The correction factor module  104  then provides the new K 1  and K 2  value to the prediction scaling module  101 . 
         [0031]    Since network management system statistics are associated with sectors, it is also possible to correct predictions depending on which sector dominance area the pixels to be scaled are located in. In this case, the prediction correction can be, for example, K 1  (area)+K 2  (area)*log (distance). In other words, each predetermined area would have corresponding correction variables K 1  and K 2 . This type of correction allows more flexibility in matching RSSI and IM predictions but may create prediction discontinuities between different dominance areas. According to exemplary embodiments, the prediction statistics module  102  computes the new sector dominance areas after prediction scaling. An RSSI probability distribution per pixel is computed on each sector dominance area. The distribution may be calculated over the same RSSI intervals used the by network management system. 
         [0032]    An IM is computed based on average signal-to-interference ratio, probability of signal-to-interference ratio falling below a certain threshold, or a similar metric. This measurement may use the same threshold definitions used in the network management system. Time advance probability distribution is computed on each sector dominance area as the percentage of pixels at the different distance intervals from the BTS. The distance intervals for time advance distribution may be fixed and mobile technology dependant. 
         [0033]      FIG. 2  is a schematic diagram illustrating a traffic map sector  200 , according to exemplary embodiments. The traffic map sector  200  includes four time advance zones: zone  201 , zone  202 , zone  203 , and zone  204 . The traffic map value corresponding to each zone is equal to the time advance value for the zone divided by the area of the zone. For example, the traffic map value for zone  202  is equal to the time advance value for zone  202  divided by the area of zone  202 . 
         [0034]    A traffic map may be considered when computing prediction statistics. A traffic map is often unknown and can be a significant source of uncertainty. The traffic map derivation module  105  can be used to provide an estimated traffic map based on time advance distribution information provided by the NMS and on scaled predictions provided by the prediction scaling module  101 . 
         [0035]    The units for calculating traffic map intensity may be, for example, Erlangs. An Erlang is a dimensionless unit used in telephony as a statistical measure of the volume of telecommunication traffic. A time advance distribution defines an amount of traffic at different distance intervals from a base transceiver station (BTS). In Global System for Mobile communications (GSM) systems, distance intervals of, for example, 550 meters may be used. A traffic map can be derived by dividing each NMS time advance value by the number of pixels in the corresponding time advance area. 
         [0036]      FIG. 3  is a block diagram illustrating an example of calculating an IM error metric applicable to individual sectors. The error measurement module  3  compares the predicted RSSI, IM and time advance values with corresponding values provided by the NMS. For example, rows and columns from a first IM  310  provided by the NMS may be compared with corresponding rows and columns from a second IM  320  that is based on predicted values. An IM row error represents the error in the interference generated to the rest of the sectors by a particular sector. An IM column error represents the error of the interference suffered by a particular sector from the rest of the sectors. As an example, a row  311  from the first IM  310  is compared with a corresponding row  321  from the second IM  320  to determine a sector row error. Similarly, a column  312  from the first IM  310  is compared with a corresponding column  322  from the second IM  320  to determine a sector column error. RSSI and TA errors per sector may also computed based on comparisons of predicted RSSI values and RSSI values received from the NMS. A global error metric can be computed as a weighted combination of RSSI, IM and TA errors as illustrated, for example, in  FIG. 4 . 
         [0037]      FIG. 4  is a flow diagram illustrating an example of global error calculation, according to exemplary embodiments. A global error metric may be defined as a weighted addition of RSSI, IM and time advance errors. By setting different weights it is possible to obtain a better matching of some statistics at the expense of the others. In the example shown in  FIG. 4 , an IM row error  402  is multiplied by a row error weight  404  to determine a weighted IM row error  406 . The IM column error  408  is multiplied by a column error weight  410  to determine a weighted IM column error  412 . The weighted IM row error  406  is added to the weighted IM column error  412  to determine the IM error  414 . The IM error  414  is multiplied by an IM error weight  416  to determine a weighted IM error  418 . The RSSI error  420  is multiplied by an RSSI error weight  422  to determine a weighted RSSI error  424 . A TA error  426  is multiplied by a TA error weight  428  to determine a weighted TA error  430 . The weighted IM error  418 , the weighted RSSI error  424 , and the weighted TA error  430  are then summed to determine the global error  432 . 
         [0038]      FIG. 5  is a table illustrating a solution area  500 , according to exemplary embodiments. As mentioned above, a correction factor can be equal to K 1 +K 2 *log (distance). The prediction correction factor module  104  searches K 1  and K 2  values per sector that minimize the global error as measured by the error measurement module  103 . Searching systematically for the optimum K 1  and K 2  values thorough all possible sectors may or may not be practical, depending on computing capacity. For example for a  300  sector network and fifteen possible values for K 1  and K 2 , the number of evaluations is equal to 47,500. 
         [0039]      FIG. 6  is a table illustrating an iterative method for determining optimum K 1  and K 2  values for the solution area  500  shown in  FIG. 5 , according to exemplary embodiments. For each sector, a two-dimensional sliding window  602  is used. An algorithm iterates over all sectors following, for example, either a random or a predetermined order. Optimum K 1  and K 2  values inside the sliding window  602  are found by systematically evaluating the error for each pair of K 1  and K 2  values. The sliding window  602  for each sector is updated after each iteration so that the center of the window is the local minimum of the error. After a number of iterations or when the sliding window cannot be moved within the table so as to be centered on a local minimum, the process stops. 
         [0040]      FIG. 7  is a flow chart illustrating a routine  700  for scaling predictions for signal propagation, in accordance with exemplary embodiments. As implemented at operation  701 , the prediction scaling module  101  computes scaled predictions for signal propagation based on correction factors received from the prediction correction factor module  104  and on original propagation predictions. According to exemplary embodiments, the prediction scaling module  101  may use the following formula: scaled predictions (azimuth, distance)=original predictions (azimuth, distance)+K 1 +K 2 *log 10  (distance), where K 1  and K 2  are correction factors that can have positive or negative values. 
         [0041]    Note that alternative propagation scaling formulas may be used. Since network management system statistics are associated with sectors, it is also possible to correct predictions depending on which sector dominance area the pixels to be scaled are located in. In this case, the prediction correction can be, for example, K 1  (area)+K 2  (area)*log (distance). 
         [0042]    As implemented at operation  702 , the prediction scaling module  101  provides the scaled predictions for signal propagation to the prediction statistics module  102 . Then, as implemented at operation  703 , the prediction statistics module  102  computes estimates for received signal strength indicator (RSSI), interference matrix (IM), and/or timing advance (TA) values based on the scaled predictions from the prediction scaling module  101  and on a traffic map. The traffic map received by the prediction statistics module  102  may be an actual traffic map or an estimated traffic map. An optional traffic map derivation module  105  may be used to provide an estimated traffic map to the prediction statistics module  102 . 
         [0043]    As implemented at operation  704 , the prediction statistics module provides the estimates for RSSI, IM, and TA values to the error measurement module  103 . The error measurement module  103  then computes an error metric based on a comparison of estimates for RSSI, IM and/or TA values with corresponding values received from the NMS, as implemented at operation  705 . The error metric may be based on a weighted combination of RSSI, IM, and/or TA errors. 
         [0044]    The error measurement module then provides the error metric to the prediction correction factor module  104 , as implemented at operation  706 . The prediction correction factor module  104  uses error metric to select new correction factor values K 1  and K 2 , as implemented at operation  707 . A determination is then made as to whether optimal K 1  and K 2  scaling factors have been identified, as implemented at operation  708 . If optimal K 1  and K 2  scaling factors have been identified, then the routine  700  ends. If optimal K 1  and K 2  scaling factors have not been identified, then the method  700  returns to operation  701 , where the prediction scaling module  101  computes revised scaled predictions based on the new K 1  and K 2  values. 
         [0045]      FIG. 8  is a flow chart illustrating an operation  800  for determining optimum correction factors. As implemented at operation  801 , a sector iteration order is defined. A new sector is then selected, as implemented at operation  802 . New K 1  and K 2  values are selected from a sliding window, as implemented at operation  803 . An example of a sliding window is shown in  FIG. 6 . An error corresponding to the selected K 1  and K 2  values is then computed, as implemented at operation  804 . A determination is then made at operation  805  as to whether all K 1  and K 2  values in the sliding window have been evaluated, as implemented at operation  805 . 
         [0046]    If it is determined that not all K 1  and K 2  values in the sliding window have been evaluated, then the method returns to operation  803  where new K 1  and K 2  values are selected from the sliding window. However, if it is determined that all K 1  and K 2  values in the sliding window have been evaluated, then the method proceeds to operation  806  where the best K 1  and K 2  values are restored, and the sliding window is updated. A determination is then made as to whether there are more sectors to be evaluated, as implemented at operation  807 . 
         [0047]    If a determination is made that there are more sectors to be evaluated, then the routine  800  returns to operation  802  where a new sector is selected. If, however, a determination is made at operation  808  that there are no more sectors to be evaluated, then a determination is made as whether a total number of iterations has been exceeded. If it is determined that a total number of iterations has not been exceeded, then the routine  800  returns to operation  801 , where a sector iteration order is defined. If, however, it is determined that a total number of iterations has been exceeded, then the routine  800  is terminated. 
         [0048]    In cases where the predictions are inaccurate and because prediction correction is based on a statistical matching, some sectors may end up with unrealistic predictions and/or dominance area size. In order to avoid this problem, the same correction factor may initially be applied to all sectors in a network. After a certain time period, the same correction factor may then be applied to sectors belonging to a common site. Eventually, correction factors may be applied individually to each sector such that each sector may have a different correction factor. 
         [0049]      FIG. 9  is a block diagram illustrating a computer  900  capable of executing the software components presented herein. The computer  900  includes a central processing unit (CPU)  902 , a system memory  908 , including a random access memory (RAM)  914  and a read-only memory (ROM)  916 , and a system bus  904  that couples the memory  908  to the CPU  902 . A basic input/output system containing the basic routines that help to transfer information between elements within the computer  900 , such as during startup, is stored in the ROM  916 . The computer  900  further includes a mass storage device  910  for storing an operating system  920  and other program modules, which will be described in greater detail below. 
         [0050]    The mass storage device  910  is connected to the CPU  902  through a mass storage controller (not shown) connected to the bus  904 . The mass storage device  910  and its associated computer-readable media provide non-volatile storage for the computer  900 . Although the description of computer-readable media contained herein refers to a mass storage device, such as a hard disk or CD-ROM drive, it should be appreciated by those skilled in the art that computer-readable media can be any available media that can be accessed by the computer  900 . 
         [0051]    By way of example, and not limitation, computer-readable media may include volatile and non-volatile, removable and non-removable media implemented in any method or technology for storage of information such as computer-readable instructions, data structures, program modules or other data. For example, computer-readable media includes, but is not limited to, RAM, ROM, EPROM, EEPROM, flash memory or other solid state memory technology, CD-ROM, digital versatile disks (DVD), HD-DVD, BLU-RAY, or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can be accessed by the computer  900 . 
         [0052]    The computer  900  may connect to a network through a network interface unit  906  connected to the bus  904 . It should be appreciated that the network interface unit  906  may also be utilized to connect to other types of networks and remote computer systems. The computer  900  may also include an input/output controller  912  for receiving and processing input from a number of other devices, including a keyboard, mouse, or electronic stylus (not shown in  FIG. 9 ). Similarly, an input/output controller may provide output to a display screen, a printer, or other type of output device (also not shown in  FIG. 9 ). 
         [0053]    As mentioned briefly above, a number of program modules and data files may be stored in the mass storage device  910  and RAM  914  of the computer  900 , including the operating system  920  suitable for controlling the operation of the computer  900 . The mass storage device  910  and RAM  914  may also store one or more program modules. In particular, the mass storage device  910  and the RAM  914  may store a scaling system  100 . The scaling system  100  may include a prediction scaling module  101 , a prediction statistics module  102 , an error measurement module  103 , and a prediction correction factor module  104 , as shown in  FIG. 1 . These modules  101 - 104  may be configured to operate as illustrated, for example, in  FIG. 7 . Other program modules may also be stored in the mass storage device  910  and utilized by the computer  900 . 
         [0054]    It should be appreciated that, in the extreme case where the propagation correction factor is different for each pixel, it is possible to scale individual RSSI pixel values without affecting to other pixels. This case is, therefore, referred to as “pixel scaling” instead of “propagation model scaling” as described above. Virtually any OSS counter, like RSSI and IM probability distribution, may be matched by performing pixel scaling. In particular, matching may be performed by defining the RSSI values per pixel that result in a match with OSS statistics. 
         [0055]    The OSS statistics are known inside the dominance area of the strongest server. Consider, for example, a dominance area of N pixels. There are many different ways to assign N RSSI values to N pixels. According to embodiments, this may be done following different algorithms and, depending on the information available, based on a most probably location principle. For example, lowest scaled RSSI values may be assigned to pixels with lowest predicted RSSI values. 
         [0056]    Some OSS statistics are not a direct measure of RSSI values, but are influenced by them. For example, C/I distributions in GSM systems or Ec/Io distributions in UMTS systems. In those cases, the N values that match the C/I or Ec/Io distribution are identified and, in a second phase, the RSSI pixel values that result in the N scaled C/I or Ec/Io pixel values are located. 
         [0057]    One example of pixel scaling for GSM system is described below. In this embodiment, the objective is to identify RSSI pixel values for serving cells and the interferers that match RxLEV and C/I distributions reported by the OSS. OSS statistics are computed in a dominance area. Therefore, the number of RSSI and C/I samples coincides with the number of pixels of the dominance area. For a dominance area with N pixels the following samples are found: N RSSI values of serving cell that matches with serving cell level distribution; N C/I values that matches with C/I distribution of interferer  1 ; N C/I values that matches with C/I distribution of interferer  2 ; N C/I values that matches with C/I distribution of interferer  3 ; and so on. Algorithms for finding a number of samples that match optimally with a specific probability distribution are known to those in the art. 
         [0058]    According to embodiments, the N RSSI values may then be assigned to pixels in the dominance area. The lowest RSSI value is assigned to the pixel with the lowest predicted RSSI values, which is considered to be scaled. This process is repeated until all N values have been assigned to all available pixels (all pixels are scaled). While scaling RSSI values of the serving cell, all interferers are scaled up or down in order to keep C/I per pixel unchanged. A similar process may be applied to the N C/I values for each interferer. In this case, the assigning criteria is predicted C/I values. After C/I is scaled, the RSSI value for an interferer can be found as RSSIinterferer [dBm]=RSSIserving [dBm]−C/I at each pixel. 
         [0059]    The pixel scaling process for best server RSSI and one of the interferers is depicted in  FIG. 10 . A comparison of OSS C/I statistics vs. predicted C/I before and after pixel scaling is depicted in  FIG. 11 . Note that because of the limited number of pixels in the dominance area, the matching is not perfect for some interferer-victims relationships. 
         [0060]    It should also be appreciated that, after implementing antenna changes in a real network, the OSS statistics will change. The estimation of this change is important for wireless network optimization. One way to accomplish this is to re-compute new predictions after antenna changes with the pixel scaled path-loss. 
         [0061]    Although the subject matter presented herein has been described in conjunction with one or more particular embodiments and implementations, it is to be understood that the embodiments defined in the appended claims are not necessarily limited to the specific structure, configuration, or functionality described herein. Rather, the specific structure, configuration, and functionality are disclosed as example forms of implementing the claims. Various modifications and changes may be made to the subject matter described herein without following the example embodiments and applications illustrated and described, and without departing from the true spirit and scope of the embodiments, which is set forth in the following claims.