Abstract:
According to an aspect of an embodiment, a base station includes a first interface, a second interface, a third interface, and an allocator. The first interface communicates with a plurality of terminals via a licensed radio spectrum. The second interface communicates with the plurality of terminals via an unlicensed radio spectrum. The third interface receives from a central controller a licensed radio spectrum assignment including a set of assigned physical resource blocks associated with the licensed radio spectrum. The allocator allocates unlicensed radio spectrum resources and the physical resource blocks among the plurality of terminals.

Description:
FIELD 
     The embodiments discussed herein are related to radio resource control. 
     BACKGROUND 
     Increasing popularity of smart phones and other mobile devices, together with increasing use of mobile internet applications have led to an exponential growth of data rate demands on cellular systems generally employing licensed radio spectrum (“licensed spectrum”) resources. At the same time, limited spectrum resources are available to allow mobile network operators (MNOs) to meet current and future data rate demands. 
     The MNOs are further faced with the challenge of poor indoor coverage, particularly at an edge of a telecommunication system cell. Poor indoor coverage may be a significant challenge for MNOs, as most data traffic and voice calls originate from indoors. 
     To address the challenges of meeting ever-increasing data rate demands and poor indoor coverage, some proposed solutions include an increased reliance on femtocells. Generally, femtocells are small-range, low-power cells that may be deployed to enhance indoor coverage and offload some traffic from a macrocell. Offloading traffic to the femtocell may reduce congestion in the macrocell network and thus may help improve the experience for users connected to the telecommunication system via the macrocell. Like femtocells, other small cells such as picocells may also be used to reduce macrocell congestion and/or improve indoor coverage. 
     Concurrently, public IEEE 802.11 wireless hotspots have grown in number to provide internet access to customers over ever-increasing areas. Generally, IEEE 802.11 wireless hotspots provide wireless internet access via unlicensed radio spectrum (“unlicensed spectrum”) resources. 
     Most modern user equipments (UE) are outfitted to communicate via both cellular technology and IEEE 802.11 technology. Furthermore, the 3rd Generation Partnership Project&#39;s (3GPP) standards provide an architecture that allows UE seamless interoperability over cellular systems and IEEE 802.11 wireless hotspots without user interaction. 
     The 3GPP has presented a few approaches to offload licensed spectrum traffic to an unlicensed spectrum in the Long Term Evolution (LTE) standards. A Local Internet Protocol (IP) Access (LIPA) approach allows a UE to access a local residential or corporate network through a 3GPP device—such as a femtocell—without employing the MNO&#39;s core network. A Selected IP Traffic Offload (SIPTO) approach allows UE traffic to flow from the 3GPP device directly to the internet via a local packet gateway (L-PGW), thus bypassing the MNO&#39;s core network. Both the LIPA and SIPTO approaches are transparent to UE and intend to avoid congestion in the MNO&#39;s core network. Furthermore, in the LIPA and SIPTO approaches, traffic at the UE occurs over the licensed spectrum via the UE&#39;s 3GPP radio. An IP Flow Mobility (IFOM) approach leverages the UE to determine whether to use a 3GPP device via the licensed spectrum, e.g. LTE, or an IEEE 802.11 access point (AP) via the unlicensed spectrum. Unlike the LIPA and SIPTO approaches, the IFOM is radio access network (RAN) transparent, and not UE transparent. 
     The subject matter claimed herein is not limited to embodiments that solve any disadvantages or that operate only in environments such as those described above. Rather, this background is only provided to illustrate one example technology area where some embodiments described herein may be practiced. 
     SUMMARY 
     According to an aspect of an embodiment, a base station includes a first interface, a second interface, a third interface, and an allocator. The first interface communicates with a plurality of terminals via a licensed radio spectrum. The second interface communicates with the plurality of terminals via an unlicensed radio spectrum. The third interface receives from a central controller a licensed radio spectrum assignment including a set of assigned physical resource blocks associated with the licensed radio spectrum. The allocator allocates unlicensed radio spectrum resources and the licensed spectrum physical resource blocks among the plurality of terminals. 
     The object and advantages of the embodiments will be realized and achieved at least by the elements, features, and combinations particularly pointed out in the claims. 
     It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are not restrictive of the invention, as claimed. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Example embodiments will be described and explained with additional specificity and detail through the use of the accompanying drawings in which: 
         FIG. 1  is a diagrammatic view of an example network architecture of a telecommunication system; 
         FIG. 2  is a diagrammatic view of a telecommunication system including a central controller and a base station; 
         FIG. 3  is a flowchart of an example load estimation method; 
         FIG. 4  is a flowchart of an example graph coloring method; and 
         FIG. 5  is a flowchart of an example method of controlling radio resources. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Femtocells and other small cells may be used in a number of environments. It may be desirable to employ a high density of femtocells in environments that experience a high number of mobile devices and/or high requested data rates in a relatively small area, generally described herein as enterprise environments. Enterprise environments may include corporate premises, shopping complexes, stadiums, arenas, conference venues, dense residential regions, dense commercial regions, heavily trafficked urban regions, and the like. 
     When multiple femtocells or other small cells are deployed in a relatively small area, interference between neighboring femtocells may present a major challenge. Particular femtocells may accommodate both licensed radio spectrum (“licensed spectrum”) and unlicensed radio spectrum (“unlicensed spectrum”) traffic. Femtocells that may accommodate licensed spectrum and unlicensed spectrum traffic are generally described herein as dual-access-technology femtocells. Similarly, dual-access-technology cells may refer to any cell that may accommodate both licensed and unlicensed spectrum traffic. 
     Studies have been done on interference control between cells and on resource allocation between licensed and unlicensed spectrums. However, such studies have failed to consider dual-access-technology cells in enterprise environments. Some have considered cellular-spectrum-only femtocells in enterprise environments. Others have considered licensed and unlicensed spectrum management of a single dual-access-technology femtocell. These are generally not extendable to wide deployment of dual-access-technology cells, and are particularly not extendable to dual-access-technology femtocells or other small cells in enterprise environments. 
     Advantageously, embodiments described herein may allow dual-access-technology femtocells and other small cells to be successfully deployed in enterprise environments. Embodiments described herein may advantageously increase throughput and achieve fairness for most, if not all, network users. However, the techniques described herein may be expanded beyond dual-access-technology femtocells. Generally, the embodiments described herein may be employed in other settings where multiple types of radio spectrum resources are available and accessible by multiple devices. 
     Some embodiments as herein described may relate to a communication system based on the 3rd Generation Partnership Project&#39;s (3GPP) Long Term Evolution (LTE) radio access network. Descriptions involving LTE may also apply to 3GPP&#39;s Long Term Evolution Advanced (LTE-A) radio access network or Worldwide Interoperability for Microwave Access (WiMAX) radio access network. However, the embodiments described herein are not limited to the example communication systems described. Rather, the embodiments described herein may be applicable to other communication systems. 
     Embodiments of the present invention will be explained with reference to the accompanying drawings. 
       FIG. 1  is a diagrammatic view of an example network architecture of a telecommunication system  100 . In some embodiments, the network architecture may include the network architecture of an Evolved Universal Mobile Telecommunications System (E-UMTS). The E-UMTS may include an LTE radio access network or the like. The radio access network may include an E-UMTS Terrestrial Radio Access Network (eUTRAN). However, other types of network architecture may be used. 
     The telecommunication system  100  may include multiple base stations, designated generally as a first base station  104   a  up to an Nth base station  104   b  (collectively “base stations  104 ”). The base stations  104  may include base station equipment, including hardware and/or software for allowing radio communication with radio-communication-equipped nodes (“wireless nodes”). The base stations  104  may generally allow wireless nodes to wirelessly communicate with each other, and/or to wirelessly access a core network and/or an internet protocol (IP) network, or the like. 
     In some embodiments, the base stations  104  include multiple small cell base stations  104  deployed in an enterprise setting. For example, the base stations  104  may include multiple femtocells such as home eNodeBs (HeNBs) located in a close geographic region such as corporate premises, shopping complexes, stadiums, arenas, conference venues, dense residential regions, dense commercial regions, heavily trafficked urban regions, and the like. 
     In general, the base stations  104  may include hardware and software allowing radio communication over both a licensed spectrum and an unlicensed spectrum. The licensed spectrum may generally include portions of a radio spectrum licensed for transmission of cellular data. For example, the base stations  104  may be configured to transmit cellular data that complies with an LTE, such as 3GPP specification releases 8-12. The unlicensed spectrum may generally include portions of a radio spectrum set aside for license-free wireless communications. For example, the base stations  104  may be configured to communicate via an IEEE 802.11 interface or other wireless communication interface. 
     The base stations  104  may communicate with a central controller  102  via interfaces formed between the base stations  104  and the central controller  102 . For example, Interface  105   a  may be formed between the first base station  104   a  and the central controller  102  and interface  105   b  may be formed between the N-th base station  104   b  and the central controller  102 . Interface  105   a  and interface  105   b  (collectively “interfaces  105 ”) may include wired connections, but in some instances interfaces  105  may alternately include wireless connections. As disclosed herein, the central controller  102  may assist in interference management between base stations  104  and/or in resource management in the licensed spectrum such that the base stations  104  may be deployed in an enterprise environment. 
     The base stations  104  may generally include processors  107   a  and  107   b  (collectively “processors  107 ”) and memory  109   a  and  109   b  (collectively “memory  109 ”). Instructions may be stored on the memory  109 . When the instructions are executed by the processors  107 , the base stations  104  may perform operations related to and/or including the processes described herein. 
     The telecommunication system  100  may include multiple wireless nodes communicating with the base stations  104  over licensed and/or unlicensed spectrums. Wireless nodes that may communicate over both licensed and unlicensed spectrums are generally described herein as terminals. For example, terminals may include smartphones that allow LTE cellular communication, as well as IEEE 802.11 communication. Wireless nodes configured to communicate over only unlicensed spectrums are generally described herein as devices. For example, devices may include laptop computers that allow IEEE 802.11 communication, but are not equipped for cellular communication, or have temporarily disabled cellular communication. 
     As disclosed in  FIG. 1 , multiple terminals  110   a ,  110   b ,  110   c , and  110   d  (collectively “terminals  110 ”) may be associated with the base stations  104 . For example, a first terminal  110   a  (designated as terminal 1 1 ) through an S 1 -th terminal  110   b  (designated as terminal S 1 ) may be associated with the first base station  104   a.    
     The terminals  110  may form licensed spectrum interfaces  106   a  and  106   b  (collectively “licensed spectrum interfaces  106 ”) with their associated base stations  104 . Similarly, the terminals  110  may form unlicensed spectrum interfaces  108   a  and  108   b  (collectively “unlicensed spectrum interfaces  108 ”) with their associated base stations  104 . For example, the first terminal  110   a  through the S 1 -th terminal  110   b  may form licensed spectrum interfaces  106   a  and unlicensed spectrum interfaces  108   a  with the first base station  104   a . The terminals  110  may also experience interference  114   a  and  114   b  (collectively “interference  114 ”) from unassociated base stations  104 , generally in the licensed spectrum. The licensed spectrum interfaces  106  and the unlicensed spectrum interfaces  108  are generally wireless connections between the terminals  110  and the base stations  104  that allow data to be communicated between the terminals  110  and the base stations  104 . 
     Multiple devices  112   a ,  112   b ,  112   c , and  112   d  (collectively “devices  112 ”) may be associated with the base stations  104 . For example, a first device  112   a  (designated as device 1 1 ) through a W 1 -th device  112   b  (designated as device W 1 ) may be associated with the first base station  104   a . The devices  112  may form unlicensed spectrum interfaces  108  with their associated base stations  104 . For example, the first device  112   a  through the W 1 -th device  112   b  may form unlicensed spectrum interfaces  108   a  with the first base station  104   a.    
     The central controller  102 , the terminals  110 , and the devices  112  may include processors and memory (not shown), analogous to the processors  107  and memory  109  of the base stations  104 . 
     Each of the terminals  110  may have a number of connections, generally with different minimum communication rate requirements. Each minimum communication rate requirement may be a function of the traffic type of each connection. For example, a terminal  110   a  may simultaneously have a conversational voice connection and a transmission control protocol (TCP) based connection. According to quality of service (QoS) requirements of each connection for each terminal  110 , the base stations  104  may set a minimum rate requirement for each of the terminals  110 . The minimum rate requirement for a particular terminal  110   a ,  110   b ,  110   c , or  110   d  may be set to the sum of the minimum rate requirements for all connections of the particular terminal  110   a ,  110   b ,  110   c , or  110   d . The minimum rate requirements may generally be attained over the licensed and/or unlicensed spectrums. 
     Embodiments described herein may be employed to achieve the minimum rate requirements for all terminals  110  in a fair way. For example, an attempt may be made to maximize the minimum rate of the terminals  110  in the telecommunication system  100 . However, different terminals  110  may have different minimum rate requirements. In some embodiments, a minimum proportional rate may be maximized, wherein the proportional rate of a particular terminal such as terminal  110   a  may be defined as a sum of the rates achieved by the terminal  110   a  over both the licensed and unlicensed spectrums for all the connections of the terminal  110   a , divided by the sum of the minimum rate requested by the terminal  110   a  for all the connections of the terminal  110   a . However, alternate objective functions may be defined depending on the preferences of MNOs. For example, an objective function may maximize the sum throughput of the entire telecommunication system  100 . An example optimization formula is described below as Formula 1. 
     The formulas disclosed herein and the related discussions are generally described with reference to downlink communication. Uplink communication may be alternately or additionally considered in an analogous manner. Furthermore, for calculations related to LTE rate calculations, Shannon capacity may be used for simplifying the disclosure. However, other rate calculations may be conducted. For example, rate calculations may account for bandwidth efficiency due to different overheads such as cyclic-prefix and pilots. Furthermore, rate calculations may account for a signal to interference plus noise ratio (SINR) implementation efficiency due to receiver algorithms and supported modulation-coding schemes (MCS). 
     A number of the variables used in Formula 1 and/or other formulas disclosed herein are described below. Additional variables may be described in association with a particular formula and/or may be understood from the variable&#39;s context. 
     Variable N represents the number of base stations  104 . Variable n represents the particular base stations  104 ; thus, n is generally a set of integers between 1 and N, inclusive. 
     S n  represents the number of terminals  110  with both licensed spectrum interfaces  106  and unlicensed spectrum interfaces  108  connected to base station n. S represents the total number of terminals  110  in the network, i.e., the sum of S n  for all N base stations  104 . In Formula 1, i generally represents the particular terminals  110  of the entire telecommunication system  100 ; thus, for Formula 1, i is generally within a set of integers between 1 and S, inclusive. However, in all other formulas, i generally represents the particular terminals associated with a particular base station n; thus, for other formulas, i is generally within a set of integers between 1 and S n , inclusive. 
     c represents a connection for a terminal. C i   (n)  represents a set of connections c for terminal i associated with base station n. 
     W n  represents the number of devices  112  with only an unlicensed spectrum interface  108  connected to base station n. W represents the total number of devices  112  in the network, i.e., the sum of W n  for all N base stations  104 . Device j generally represents the particular devices associated with a particular base station n; thus, j is generally within a set of integers between 1 and W n , inclusive. 
     P max   (n)  represents the maximum transmission power of base station n. 
     K represents a total number of physical resource blocks (PRBs) associated with the licensed spectrum. Physical resource block k generally represents a particular PRB; thus, k is generally within a set of integers between 1 and K, inclusive. However, in some instances, k may represent one or more subcarriers of the PRBs. 
     P i,k   (n)  represents the transmission power from base station n to terminal i on PRB k. 
     h i,k   (n)  represents channel gain from base station n to terminal i on PRB k. 
     σ 2  represents noise variance per PRB in the licensed spectrum. 
     B represents total system bandwidth. 
     R AP   (n)  represents a maximum throughput that base station n may get in the downlink via the unlicensed spectrum. Each of the base stations  104  may generally calculate R AP   (n)  given the total number of stations contending for resources on the unlicensed spectrum. In embodiments employing IEEE 802.11 as the unlicensed spectrum, IEEE 802.11 medium access control (MAC) performance may be heavily dependent on the number of stations contending for resources on the unlicensed spectrum. For example, stations contending for unlicensed spectrum resources at the first base station  104   a  may include the first base station  104   a , the first device  112   a  through the W-th device  112   b , and the first terminal  110   a  through the S-th terminal  110   b , although some terminals may not contend for any unlicensed spectrum resources. Thus, if all terminals associated with base station n are transmitting to the base station n on the unlicensed spectrum, the total number of contending stations will equal S n +W n +1. In some embodiments, if a relatively large number of devices  112  connect to a base station  104   a , the base station  104   a  may deactivate the unlicensed spectrum connectivity of some terminals  110  to reduce the contention for the unlicensed spectrum resources. 
     In some embodiments, it is assumed that each of the base stations  104  operate on different unlicensed spectrum channels, or at least that neighboring base stations use different unlicensed spectrum channels while the same unlicensed spectrum channel may be reused for a distant base station within the set of base stations  104 , similar to the frequency reuse concept in mobile cellular communication. As a result, the contention on the unlicensed spectrum of a base station from devices or terminals connected to other base stations may be ignored. Such an assumption may be reasonable since a device or terminal usually tries to contend on the unlicensed spectrum channel with strongest received signal power, which is generally coming from the nearest base station. However, this assumption, as well as other assumptions described herein, may be made to simplify the presentation of some embodiments, but do not limit the disclosure. For example, even when it is assumed that all devices and terminals may contend on any unlicensed spectrum of any of the base stations  104 , or that all base stations  104  use the same unlicensed spectrum channel, the embodiments described herein may still be applicable. 
     R w,j   (n)  represents a requested downlink data rate of a device j connected to base station n in the unlicensed spectrum. 
     RU i,c   (n)  represents an estimated downlink data rate in the unlicensed spectrum assigned to the connection c of the terminal i associated with base station n. 
       r   i,c   (n)  represents a minimum rate requirement for connection c for terminal i associated with base station n. 
     w i,c   (n)  represents the number of PRBs assigned to the connection c of the terminal i associated with base station n. 
     Ω n  represents a set of terminals connected to base station n. 
                   n  represents a set of PRBs assigned to base station n.
     
       
         
           
             
               
                 
                   
                     FORMULA 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     max 
                     
                       { 
                       
                         
                           Ω 
                           n 
                         
                         , 
                         
                           p 
                           
                             i 
                             , 
                             k 
                           
                           
                             ( 
                             n 
                             ) 
                           
                         
                         , 
                         
                           RU 
                           
                             i 
                             , 
                             c 
                           
                         
                       
                       } 
                     
                   
                   ⁢ 
                   
                     
                       min 
                       i 
                     
                     ⁢ 
                     
                       
                         1 
                         
                           
                             ∑ 
                             
                               c 
                               ∈ 
                               
                                 C 
                                 i 
                               
                             
                           
                           ⁢ 
                           
                             
                               r 
                               _ 
                             
                             
                               i 
                               , 
                               c 
                             
                           
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               ∑ 
                               
                                 k 
                                 = 
                                 1 
                               
                               K 
                             
                             ⁢ 
                             
                               
                                 B 
                                 K 
                               
                               ⁢ 
                               
                                 
                                   log 
                                   2 
                                 
                                 ( 
                                 
                                   1 
                                   + 
                                   
                                     
                                       
                                         p 
                                         
                                           i 
                                           , 
                                           k 
                                         
                                         
                                           ( 
                                           n 
                                           ) 
                                         
                                       
                                       ⁢ 
                                       
                                         h 
                                         
                                           i 
                                           , 
                                           k 
                                         
                                         
                                           ( 
                                           n 
                                           ) 
                                         
                                       
                                     
                                     
                                       
                                         σ 
                                         2 
                                       
                                       + 
                                       
                                         
                                           ∑ 
                                           
                                             m 
                                             ≠ 
                                             n 
                                           
                                         
                                         ⁢ 
                                         
                                           
                                             p 
                                             
                                               i 
                                               , 
                                               k 
                                             
                                             
                                               ( 
                                               m 
                                               ) 
                                             
                                           
                                           ⁢ 
                                           
                                             h 
                                             
                                               i 
                                               , 
                                               k 
                                             
                                             
                                               ( 
                                               m 
                                               ) 
                                             
                                           
                                         
                                       
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                           + 
                           
                             
                               ∑ 
                               
                                 c 
                                 ∈ 
                                 
                                   C 
                                   i 
                                 
                               
                             
                             ⁢ 
                             
                               RU 
                               
                                 i 
                                 , 
                                 c 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   1 
                   ⁢ 
                   a 
                 
               
             
             
               
                 
                   
                     
                       subject 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       to 
                       ⁢ 
                       
                         : 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           ∑ 
                           
                             k 
                             = 
                             1 
                           
                           K 
                         
                         ⁢ 
                         
                           
                             ∑ 
                             
                               i 
                               ∈ 
                               
                                 Ω 
                                 n 
                               
                             
                           
                           ⁢ 
                           
                             p 
                             
                               i 
                               , 
                               k 
                             
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                       
                     
                     ≤ 
                     
                       P 
                       max 
                       
                         ( 
                         n 
                         ) 
                       
                     
                   
                   , 
                   
                     ∀ 
                     n 
                   
                 
               
               
                 
                   1 
                   ⁢ 
                   b 
                 
               
             
             
               
                 
                   
                     
                       
                         ∑ 
                         
                           i 
                           ∈ 
                           
                             Ω 
                             n 
                           
                         
                       
                       ⁢ 
                       
                         
                           ∑ 
                           
                             c 
                             ∈ 
                             
                               C 
                               i 
                             
                           
                         
                         ⁢ 
                         
                           RU 
                           
                             i 
                             , 
                             c 
                           
                         
                       
                     
                     ≤ 
                     
                       
                         R 
                         AP 
                         
                           ( 
                           n 
                           ) 
                         
                       
                       - 
                       
                         
                           ∑ 
                           
                             j 
                             = 
                             1 
                           
                           
                             W 
                             n 
                           
                         
                         ⁢ 
                         
                           R 
                           
                             w 
                             , 
                             j 
                           
                           
                             ( 
                             n 
                             ) 
                           
                         
                       
                     
                   
                   , 
                   
                     ∀ 
                     n 
                   
                 
               
               
                 
                   1 
                   ⁢ 
                   c 
                 
               
             
             
               
                 
                   
                     
                       p 
                       
                         i 
                         , 
                         k 
                       
                       
                         ( 
                         n 
                         ) 
                       
                     
                     ≥ 
                     0 
                   
                   , 
                   
                     ∀ 
                     i 
                   
                   , 
                   k 
                   , 
                   n 
                 
               
               
                 
                   1 
                   ⁢ 
                   d 
                 
               
             
             
               
                 
                   
                     
                       RU 
                       
                         i 
                         , 
                         c 
                       
                     
                     ≥ 
                     0 
                   
                   , 
                   
                     ∀ 
                     i 
                   
                   , 
                   
                     ∀ 
                     
                       c 
                       ∈ 
                       
                         C 
                         i 
                       
                     
                   
                 
               
               
                 
                   1 
                   ⁢ 
                   e 
                 
               
             
             
               
                 
                   
                     
                       ⋃ 
                       
                         n 
                         = 
                         1 
                       
                       N 
                     
                     ⁢ 
                     
                       Ω 
                       n 
                     
                   
                   ⊆ 
                   
                     { 
                     
                       1 
                       , 
                       2 
                       , 
                       … 
                       ⁢ 
                       
                           
                       
                       , 
                       S 
                     
                     } 
                   
                 
               
               
                 
                   1 
                   ⁢ 
                   f 
                 
               
             
             
               
                 
                   
                     
                       
                         Ω 
                         n 
                       
                       ⋂ 
                       
                         Ω 
                         m 
                       
                     
                     = 
                     ∅ 
                   
                   , 
                   
                     m 
                     ≠ 
                     n 
                   
                 
               
               
                 
                   1 
                   ⁢ 
                   g 
                 
               
             
           
         
       
     
     In Formula 1, p i,k   (n)  and h i,k   (n)  respectively represent the allocated power and the channel gain from base station n to terminal i on PRB k, or in some instances, subcarrier k. 
     Subformulas 1b-1g represent various constraints of Formula 1. For example, subformula 1b represents the total transmission power constraint of each of the base stations  104 . 
     Furthermore, subformula 1c ensures that the total unlicensed spectrum rate assigned to the terminals  110  associated with base station n is upper-bounded by the available unlicensed spectrum capacity. In order to avoid congestion on the unlicensed spectrum, it may be assumed that each base station n determines the unlicensed spectrum capacity desired to serve the W n  devices  112  first and then provides downlink transmission in the unlicensed spectrum to all or some of the S n  terminals  110  depending on the remaining unlicensed spectrum capacity. The optimization in the unlicensed spectrum is thus concerned with how each of the base stations  104  divides its rate among different terminals  110  in the downlink. The term R AP   (n) −Σ j=1   W     n   R w,j   (n)  represents the available unlicensed spectrum capacity. Available unlicensed spectrum capacity may be calculated using a number of existing theoretical formulas or practical methods, such as existing techniques for calculating available capacity in IEEE 802.11 networks. 
     Subformulas 1d and 1e ensure, respectively, non-negative transmission powers and non-negative unlicensed spectrum rates. 
     With reference to subformula 1f, if the telecommunication system  100  has enough capacity to serve all S terminals  110 , then the union of Ω n  for all N base stations  104 , may equal the set {1, 2, . . . , S}. Otherwise, some terminals  110  will not be granted admission and, therefore, the union of the sets Ω n  will be a subset of {1, 2, . . . , S} as in subformula 1f. 
     Subformula 1g ensures that each of the terminals  110  is connected to only one of the base stations  104 , i.e., subformula 1g acts to ensure that the sets Ω n  are disjoint. 
     The optimization variables in Formula 1 represent the optimal terminal and base station association through finding the set Ω n , the optimal power allocation for each terminal i in base station n and for each PRB k, i.e., p i,k   (n) , and the optimal unlicensed spectrum rate distribution to different terminals  110 , i.e., RU i,c . Finding the optimal values for these variables may indicate an optimal network-wide maximum minimum rate fairness. 
     However, Formula 1 is a non-convex mixed-integer programming problem, in part due to the binary association variables associated with Ω n . Moreover, to find the solution at a central controller  102  generally requires the central controller  102  to know the channel gains of the terminals  110  on all PRBs. As a result, solving Formula 1 may be very hard and computationally impractical in many instances. 
     In some embodiments, a sub-optimal hierarchical approach may be employed to fairly distribute licensed and unlicensed spectrum resources. The tasks associated with the sub-optimal hierarchical approach may be divided between the base stations  104  and the central controller  102 . 
     In some embodiments, each base station  104  may estimate a number of requested resources in the licensed spectrum based on the number of associated terminals  110 , the rate requirements of the terminals  110 , the channel conditions of the telecommunication system  100 , and/or the rate the terminals  110  may potentially attain via the unlicensed spectrum. Each base station  104  may provide information about the requested resources to the central controller  102 . Alternately or additionally, the central controller  102  may estimate the requested resources in the licensed spectrum for each of the base stations  104 . 
     The central controller  102  may implement interference management via graph coloring methods or the like. The central controller  102  may also implement licensed spectrum resource allocation between the base stations  104  based on the requested resources associated with each base station. 
     The base stations  104  may fine-tune the licensed spectrum resource allocation, power allocation, and unlicensed spectrum resource allocation among the terminals  110  and devices  112 . Advantageously, embodiments disclosed herein may satisfy data rate requirements and quality of service (QoS) requirements of the terminals  110  and/or devices  112 . Furthermore, embodiments may achieve fairness between the terminals  110  and/or devices  112 . 
     In some embodiments, it is assumed that each terminal  110  is associated with the base station  104  with the largest average received signal power at the particular terminal  110 . Consequently, each terminal  110  may be assumed to be associated with the base station  104  with the largest observed signal to noise ratio (SNR) at the particular terminal  110 . With such an assumption, the optimization problem outlined in Formula 1 may be easier to solve, as the binary association values Ω n  will generally be known. Similarly, in some embodiments, it is assumed that each device  112  is associated with the base station  104  with the largest average received signal power at the particular device  112  in the unlicensed spectrum. Consequently, each device  112  is assumed to be associated with the base station  104  with the largest observed SNR at the particular device  112  in the unlicensed spectrum. 
       FIG. 2  is a diagrammatic view of a telecommunication system  200  including the central controller  102  and the base station  104   a . Although the base station  104   a  is described, the description of the base station  104   a  may generally apply to any individual base station of the base stations  104  of  FIG. 1 . Thus, reference may be made to the base stations  104  although only the base station  104   a  is shown in  FIG. 2 . 
     The telecommunication system  200  may perform a number of functions described herein. In some embodiments, for example, the telecommunication system  200  may construct an interference graph  208 , perform load estimation  204 , perform graph coloring  206 , perform resource and power allocation  212 , perform packet distribution  214 , perform unlicensed spectrum scheduling  216 , and may optionally perform licensed spectrum scheduling  218 . 
     The central controller  102  may construct an interference graph  208  based on base station measurements  209  received from the base station  104   a  and/or based on terminal reports  220 . Optionally, terminals generally corresponding to the terminals  110  of  FIG. 1  may provide the terminal reports  220  to the central controller  102 . The terminal reports  220  may include Received Signal Strength Indicator (RSSI) of neighboring base stations obtained during handover processes. 
     In some embodiments, base station measurements  209  may be determined at least in part by the base station  104   a  when the base station  104   a  is powered on. The base station  104   a  may listen to neighboring base stations&#39; control channels and reference signal transmissions. From the information collected, the base station  104   a  may determine the cell identification of neighboring base stations  104  as well as determine the path loss from each of the neighboring base stations  104 . 
     The central controller  102  may construct an interference graph  208  of vertices representing base stations  104  and directed edges representing interference and/or jamming conditions between base stations  104 . In some embodiments, interference and/or jamming conditions are declared when the difference between channel gains experienced by a terminal from an associated base station and an interfering base station exceed a pre-determined threshold. As a result, weak interference signals may be neglected. Advantageously, by neglecting weak interference signals the complexity of the interference graph may be reduced and the graph coloring process described herein may be simplified. Alternately, all possible interference conditions may be considered for a directed edge between any two base stations. 
     In some embodiments, an interference graph and graph coloring  206  may be achieved in a manner similar to that described in Sadr, S.; Adve, R., “Hierarchical resource allocation in femtocell networks using graph algorithms,” 2012  IEEE International Conference on Communications  ( ICC ), pp. 4416-4420, June 2012. Alternately, graph coloring  206  may be performed via a modified iterative greedy method as disclosed herein. 
     In addition to constructing an interference graph  208 , the telecommunication system  200  may perform load estimation  204 , which may be used in graph coloring  206 . In some embodiments, the base stations  104  may perform the load estimation  204 . Alternately, the load estimation  204  for one or more of the base stations  104  may be performed by the central controller  102 . 
     In performing the load estimation, the base station  104   a  may set a minimum rate requirement for the terminals  110  associated with the base station  104   a . The minimum rate requirement may generally be attained via the licensed and/or unlicensed spectrums based on the traffic type and the capacity of the licensed and/or unlicensed spectrums. 
     In performing the load estimation  204 , the base station  104   a  may attempt to estimate the resources, i.e., PRBs, each terminal requires in the licensed spectrum to achieve each terminal&#39;s minimum rate requirement. The load estimation  204  may be based, for example, on the number of terminals associated with the base station  104   a , as well as the terminals&#39; rate requirements  205 , channel conditions, and an expected rate in the unlicensed spectrum. 
     In some embodiments, the base station  104   a  may attempt to determine the minimum number of PRBs that satisfy the requirements of the associated terminals, which may help minimize interference generated at neighboring base stations. For example, load estimation  104  may be determined using Formula 2 disclosed and discussed below. 
     
       
         
           
             
               
                 
                   
                     FORMULA 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     min 
                     
                       { 
                       
                         
                           w 
                           
                             i 
                             , 
                             c 
                           
                           
                             ( 
                             n 
                             ) 
                           
                         
                         , 
                         
                           P 
                           i 
                           
                             ( 
                             n 
                             ) 
                           
                         
                         , 
                         
                           RU 
                           
                             i 
                             , 
                             c 
                           
                           
                             ( 
                             n 
                             ) 
                           
                         
                       
                       } 
                     
                   
                   ⁢ 
                   
                     
                       ∑ 
                       
                         i 
                         ∈ 
                         
                           Ω 
                           n 
                         
                       
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           c 
                           ∈ 
                           
                             C 
                             i 
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                       
                       ⁢ 
                       
                         w 
                         
                           i 
                           , 
                           c 
                         
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   2 
                   ⁢ 
                   a 
                 
               
             
             
               
                 
                   
                     
                       
                         subject 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         to 
                         ⁢ 
                         
                           : 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           w 
                           
                             i 
                             , 
                             c 
                           
                           
                             ( 
                             n 
                             ) 
                           
                         
                         ⁢ 
                         
                           B 
                           K 
                         
                         ⁢ 
                         
                           
                             log 
                             2 
                           
                           ( 
                           
                             1 
                             + 
                             
                               
                                 
                                   P 
                                   i 
                                   
                                     ( 
                                     n 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   H 
                                   i 
                                   
                                     ( 
                                     n 
                                     ) 
                                   
                                 
                               
                               
                                 
                                   w 
                                   
                                     i 
                                     , 
                                     c 
                                   
                                   
                                     ( 
                                     n 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   σ 
                                   2 
                                 
                               
                             
                           
                           ) 
                         
                       
                       + 
                       
                         RU 
                         
                           i 
                           , 
                           c 
                         
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                     ≥ 
                     
                       β 
                       ⁢ 
                       
                         
                           
                             
                                 
                             
                             ⁢ 
                             r 
                           
                           _ 
                         
                         
                           i 
                           , 
                           c 
                         
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     ∀ 
                     
                       i 
                       ∈ 
                       
                         Ω 
                         n 
                       
                     
                   
                   , 
                   
                     ∀ 
                     
                       c 
                       ∈ 
                       
                         C 
                         i 
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   2 
                   ⁢ 
                   b 
                 
               
             
             
               
                 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       
                         S 
                         n 
                       
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           c 
                           ∈ 
                           
                             C 
                             i 
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                       
                       ⁢ 
                       
                         RU 
                         
                           i 
                           , 
                           c 
                         
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                   
                   ≤ 
                   
                     
                       R 
                       AP 
                       
                         ( 
                         n 
                         ) 
                       
                     
                     - 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           1 
                         
                         
                           W 
                           n 
                         
                       
                       ⁢ 
                       
                         R 
                         
                           w 
                           , 
                           j 
                         
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   2 
                   ⁢ 
                   c 
                 
               
             
             
               
                 
                   
                     
                       ∑ 
                       
                         i 
                         ∈ 
                         
                           Ω 
                           n 
                         
                       
                     
                     ⁢ 
                     
                       P 
                       i 
                       
                         ( 
                         n 
                         ) 
                       
                     
                   
                   ≤ 
                   
                     P 
                     max 
                     
                       ( 
                       n 
                       ) 
                     
                   
                 
               
               
                 
                   2 
                   ⁢ 
                   d 
                 
               
             
             
               
                 
                   
                     
                       ∑ 
                       
                         i 
                         ∈ 
                         
                           Ω 
                           n 
                         
                       
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           c 
                           ∈ 
                           
                             C 
                             i 
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                       
                       ⁢ 
                       
                         w 
                         
                           i 
                           , 
                           c 
                         
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                   
                   ≤ 
                   K 
                 
               
               
                 
                   2 
                   ⁢ 
                   e 
                 
               
             
             
               
                 
                   
                     
                       P 
                       i 
                       
                         ( 
                         n 
                         ) 
                       
                     
                     ≥ 
                     0 
                   
                   , 
                   
                     ∀ 
                     
                       i 
                       ∈ 
                       
                         Ω 
                         n 
                       
                     
                   
                 
               
               
                 
                   2 
                   ⁢ 
                   f 
                 
               
             
             
               
                 
                   
                     
                       w 
                       
                         i 
                         , 
                         c 
                       
                       
                         ( 
                         n 
                         ) 
                       
                     
                     ≥ 
                     0 
                   
                   , 
                   
                     ∀ 
                     
                       i 
                       ∈ 
                       
                         Ω 
                         n 
                       
                     
                   
                   , 
                   
                     ∀ 
                     
                       c 
                       ∈ 
                       
                         C 
                         i 
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   2 
                   ⁢ 
                   g 
                 
               
             
             
               
                 
                   
                     0 
                     ≤ 
                     
                       RU 
                       
                         i 
                         , 
                         c 
                       
                       
                         ( 
                         n 
                         ) 
                       
                     
                     ≤ 
                     
                       RU 
                       
                         i 
                         , 
                         c 
                         , 
                         max 
                       
                       
                         ( 
                         n 
                         ) 
                       
                     
                   
                   , 
                   
                     ∀ 
                     
                       i 
                       ∈ 
                       
                         Ω 
                         n 
                       
                     
                   
                   , 
                   
                     ∀ 
                     
                       c 
                       ∈ 
                       
                         C 
                         i 
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   2 
                   ⁢ 
                   h 
                 
               
             
           
         
       
     
     Formula 2 may minimize the total requested load, i.e., the number of PRBs, per base station n over optimization control variables w i,c   (n) , P i   (n) , and RU i,c   (n) . Variable w i,c   (n)  represents the number of PRBs assigned to terminal i connected to base station n for connection c. Variable P i   (n)  represents the average allocated power for the PRBs assigned to terminal i connected to base station n. Variable RU i,c   (n)  represents the unlicensed spectrum rate assigned to terminal i connected to base station n for connection c. 
     Formula 2 is a convex optimization problem in the optimization variables w i,c   (n) , P i   (n) , and RU i,c   (n) . Solving Formula 2 may thus be more manageable than the network-wide optimization problem defined in Formula 1. 
     In Formula 2 and the formulas that follow, the subscript i is the index of the terminal within the set of terminals connected to a particular base station n, i.e., Ω n . For example, for base station n, i is generally within a set of integers between 1 and S n , inclusive. 
     Subformula 2b represents the minimum rate requirement constraints for associated terminals, i.e., terminals in the set Ω n . The term 
               w     i   ,   c       (   n   )       ⁢     B   K     ⁢       log   2     ⁡     (     1   +         P   i     (   n   )       ⁢     H   i     (   n   )             w     i   ,   c       (   n   )       ⁢     σ   2           )             
represents the licensed spectrum rate for terminal i connected to base station n for connection c, whereas variable RU i,c   (n)  represents the rate on the unlicensed spectrum for terminal i connected to base station n for connection c.
 
     Parameter β represents a feasibility parameter and may be initially set to 1 such that the achieved rate over both the licensed and unlicensed spectrums for each connection c for each terminal i may be greater than or equal to the corresponding minimum rate requirement, represented by variable  r   i,c   (n) . However, system capacity may be insufficient to achieve such minimum rate requirements, particularly when some connections or terminals have high requested rates or when the number of terminals  110  or devices  112  is very large. As a result, Formula 2 may have no feasible solution, in part because to satisfy the rate requirements of all connections for all associated terminals, base station n will need more PRBs than are available for the particular system bandwidth. Put another way, Formula 2 may have no feasible solution when subformula 2b and subformula 2e are not simultaneously satisfiable. 
     Therefore, the requested rates for the terminals associated with base station n may be lowered such that the base station n is able to feasibly solve Formula 2. For example, the value of β may be suitably reduced. 
     In some embodiments, a suitable reduced value of β may be identified via a bisection approach. For example, if Formula 2 is infeasible when β=1, the feasibility of Formula 2 may be rechecked with β=0.5. If the problem is still infeasible, the value of β is decreased to 0.25 and the feasibility is rechecked, however, if β=0.5 results in a feasible solution, then β=0.75 is evaluated. The bisection approach may be continued until a maximum number of bisection steps or until a maximum value of β equal to or less than 1 is found. 
     Other approaches for decreasing the value of β to promote a feasible solution for Formula 2 may be employed. In some embodiments, a separate parameter β c  may be defined for each connection c depending on the QoS requirement or a QoS Class Indicator (QCI) level. The β c  parameters for connections with low-priority QCI may be decreased first. As a result, the requested rate of each connection may be adjusted separately with the trade-off of increased computational complexity. 
     Subformula 2b assumes each base station n is aware of the average channel power of each associated terminal, i.e., variable H i   (n) . Furthermore, subformula 2b assumes uniform power allocation to all the PRBs assigned to the same terminal. Because average channel power values are used, the estimated load, i.e., term Σ cεC     i       (n)   w i,c   (n) , may represent a coarse estimate of the requested terminal load. The coarse estimate of the total load per base station n may be suitable for the purpose of graph coloring  206  at the central controller  102 . In some embodiments, after graph coloring the base stations may consider channel variations in the resource and power allocation step  212 , as described herein. 
     Subformula 2c ensures the sum of the unlicensed spectrum rates assigned to the terminals of base station n is upper-bounded by the available unlicensed spectrum capacity at base station n. Subformula 2d constrains the maximum transmission power for base station n. Subformula 2e ensures that the sum of requested PRBs per base station does not exceed the total number of PRBs in the system. Subformulas 2f and 2g act to ensure, respectively, non-negative allocated power and non-negative estimated loads. 
     Subformula 2h bounds the unlicensed rate for connection c for terminal i connected to base station n with a lower bound equal to 0 and an upper bound equal to RU i,c,max   (n) . The upper bound may guarantee that the distribution of rates for each connection c for each terminal i connected to base station n is based in part on the traffic type of the connection c. 
     In embodiments employing LTE for licensed spectrum communication and IEEE 802.11 for unlicensed spectrum communication, IEEE 802.11 based communications are generally not desirable for Guaranteed Bit Rate (GBR) or delay-sensitive traffic types. In some embodiments, distribution of rates over LTE or IEEE 802.11 is performed based on the QCI, which is defined for various connection types by 3GPP. The value of QCI is generally known at the base stations for each terminal&#39;s connection type. Based on the value of QCI for each connection c of a terminal i, the base station n may set an upper bound for the unlicensed spectrum rate. 
     Table 1, shown below, includes example QCIs for various example connection types. 
     
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                   
                 Resource 
                   
                 Packet Delay 
                 Packet Error 
                   
               
               
                 QCI 
                 Type 
                 Priority 
                 Budget (ms) 
                 Loss Rate 
                 Example Services 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 GBR 
                 2 
                 100 
                 10 −2   
                 Conversational Voice 
               
               
                 2 
                 GBR 
                 4 
                 150 
                 10 −3   
                 Conversational Voice 
               
               
                   
                   
                   
                   
                   
                 (live streaming) 
               
               
                 3 
                 GBR 
                 3 
                 50 
                 10 −3   
                 Real Time Gaming 
               
               
                 4 
                 GBR 
                 5 
                 300 
                 10 −6   
                 Non-Conversational Video 
               
               
                   
                   
                   
                   
                   
                 (buffered streaming) 
               
               
                 5 
                 Non-GBR 
                 1 
                 100 
                 10 −6   
                 IMS Signalling 
               
               
                 6 
                 Non-GBR 
                 6 
                 300 
                 10 −6   
                 Video (buffered streaming), 
               
               
                   
                   
                   
                   
                   
                 TCP-based (e.g., www, 
               
               
                   
                   
                   
                   
                   
                 e-mail, chat, ftp, etc.) 
               
               
                 7 
                 Non-GBR 
                 7 
                 100 
                 10 −3   
                 Voice, Video (Live Streaming), 
               
               
                   
                   
                   
                   
                   
                 Interactive Gaming 
               
               
                 8 
                 Non-GBR 
                 8 
                 300 
                 10 −6   
                 Video (buffered streaming), 
               
               
                   
                   
                   
                   
                   
                 TCP-based (e.g., www, 
               
               
                   
                   
                   
                   
                   
                 e-mail, chat, ftp, etc.) 
               
               
                 9 
                 Non-GBR 
                 9 
                 300 
                 10 −6   
                 Video (buffered streaming), 
               
               
                   
                   
                   
                   
                   
                 TCP-based (e.g., www, 
               
               
                   
                   
                   
                   
                   
                 e-mail, chat, ftp, etc.) 
               
               
                   
               
             
          
         
       
     
     In some embodiments, the unlicensed spectrum upper bound variable, i.e., RU i,c,max   (n) , of subformula 2h may be set equal to μ QCI   r   i,c   (n) , where the value of μ QCI  depends on the QCI value such that 0≦μ QCI ≦1. The value of μ QCI  may be based on the QCI value such that traffic may relatively favor the licensed spectrum or the unlicensed spectrum. For example, for a connection with a QCI level of 1, the value of μ QCI  may be set to 0 to ensure the connection gets no IEEE 802.11 rate, i.e., the connection&#39;s rate requirement is to be fulfilled completely using LTE resources. Conversely, for a non-GBR connection with low priority, such as a connection with a QCI of 9, the base station may set α QCI  to 1 to allow the entire requested rate of the connection to be obtained over IEEE 802.11. For other types of connections, the base station may set μ QCI  to a value between 0 and 1 according to the priorities, characteristics and/or QCI of the connection. 
     The base station  104   a  outputs  207  the requested load from load estimation  204  to the central controller  102  for use in graph coloring  206 . Alternately, the load estimation  204  may be performed directly by the central controller  102 . The output  207  of the load estimation  204  may be a number, i.e.,              n , representing a sum of requested PRBs for base station  104   a . In some embodiments, a ceiling or rounding operator may be applied to            n  such that an integer number of PRBs are requested. For example,            n  may be generally defined as
     
       
         
           
             
               ℳ 
               n 
             
             = 
             
               
                 ⌈ 
                 
                   
                     ∑ 
                     
                       i 
                       ∈ 
                       
                         Ω 
                         n 
                       
                     
                   
                   ⁢ 
                   
                     
                       ∑ 
                       
                         c 
                         ∈ 
                         
                           
                             C 
                             i 
                           
                           
                             ( 
                             n 
                             ) 
                           
                         
                       
                     
                     ⁢ 
                     
                       w 
                       
                         i 
                         , 
                         c 
                       
                       
                         ( 
                         n 
                         ) 
                       
                     
                   
                 
                 ⌉ 
               
               . 
             
           
         
       
     
     In some embodiments, Formula 2 may be simplified to reduce its complexity. One simplification may include assuming uniform power assignments for all terminals and depending on the resource and power allocation  212  to assign power to the terminals. The simplified formula is disclosed as Formula 3. 
     
       
         
           
             
               
                 
                   
                     FORMULA 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     min 
                     
                       { 
                       
                         
                           w 
                           
                             i 
                             , 
                             c 
                           
                           
                             ( 
                             n 
                             ) 
                           
                         
                         , 
                         
                           RU 
                           
                             i 
                             , 
                             c 
                           
                           
                             ( 
                             n 
                             ) 
                           
                         
                       
                       } 
                     
                   
                   ⁢ 
                   
                     
                       ∑ 
                       
                         i 
                         ∈ 
                         
                           Ω 
                           n 
                         
                       
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           c 
                           ∈ 
                           
                             C 
                             i 
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                       
                       ⁢ 
                       
                         w 
                         
                           i 
                           , 
                           c 
                         
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   3 
                   ⁢ 
                   a 
                 
               
             
             
               
                 
                   
                     
                       
                         subject 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         to 
                         ⁢ 
                         
                           : 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           w 
                           
                             i 
                             , 
                             c 
                           
                           
                             ( 
                             n 
                             ) 
                           
                         
                         ⁢ 
                         
                           B 
                           K 
                         
                         ⁢ 
                         
                           
                             log 
                             2 
                           
                           ( 
                           
                             1 
                             + 
                             
                               
                                 
                                   P 
                                   max 
                                   
                                     ( 
                                     n 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   H 
                                   i 
                                   
                                     ( 
                                     n 
                                     ) 
                                   
                                 
                               
                               
                                 K 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   σ 
                                   2 
                                 
                               
                             
                           
                           ) 
                         
                       
                       + 
                       
                         RU 
                         
                           i 
                           , 
                           c 
                         
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                     ≥ 
                     
                       β 
                       ⁢ 
                       
                         
                           
                             
                                 
                             
                             ⁢ 
                             r 
                           
                           _ 
                         
                         
                           i 
                           , 
                           c 
                         
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     ∀ 
                     
                       i 
                       ∈ 
                       
                         Ω 
                         n 
                       
                     
                   
                   , 
                   
                     ∀ 
                     
                       c 
                       ∈ 
                       
                         C 
                         i 
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   3 
                   ⁢ 
                   b 
                 
               
             
             
               
                 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       
                         S 
                         n 
                       
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           c 
                           ∈ 
                           
                             C 
                             i 
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                       
                       ⁢ 
                       
                         RU 
                         
                           i 
                           , 
                           c 
                         
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                   
                   ≤ 
                   
                     
                       R 
                       AP 
                       
                         ( 
                         n 
                         ) 
                       
                     
                     - 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           1 
                         
                         
                           W 
                           n 
                         
                       
                       ⁢ 
                       
                         R 
                         
                           w 
                           , 
                           j 
                         
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   3 
                   ⁢ 
                   c 
                 
               
             
             
               
                 
                   
                     
                       ∑ 
                       
                         i 
                         ∈ 
                         
                           Ω 
                           n 
                         
                       
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           c 
                           ∈ 
                           
                             C 
                             i 
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                       
                       ⁢ 
                       
                         w 
                         
                           i 
                           , 
                           c 
                         
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                   
                   ≤ 
                   K 
                 
               
               
                 
                   3 
                   ⁢ 
                   d 
                 
               
             
             
               
                 
                   
                     
                       w 
                       
                         i 
                         , 
                         c 
                       
                       
                         ( 
                         n 
                         ) 
                       
                     
                     ≥ 
                     0 
                   
                   , 
                   
                     ∀ 
                     
                       i 
                       ∈ 
                       
                         Ω 
                         n 
                       
                     
                   
                   , 
                   
                     ∀ 
                     
                       c 
                       ∈ 
                       
                         C 
                         i 
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   3 
                   ⁢ 
                   e 
                 
               
             
             
               
                 
                   
                     0 
                     ≤ 
                     
                       RU 
                       
                         i 
                         , 
                         c 
                       
                       
                         ( 
                         n 
                         ) 
                       
                     
                     ≤ 
                     
                       RU 
                       
                         i 
                         , 
                         c 
                         , 
                         max 
                       
                       
                         ( 
                         n 
                         ) 
                       
                     
                   
                   , 
                   
                     ∀ 
                     
                       i 
                       ∈ 
                       
                         Ω 
                         n 
                       
                     
                   
                   , 
                   
                     ∀ 
                     
                       c 
                       ∈ 
                       
                         C 
                         i 
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   3 
                   ⁢ 
                   f 
                 
               
             
           
         
       
     
     Formula 3 is a linear programming problem in the variables w i,c   (n)  and RU i,c   (n) . As a result, Formula 3 may be efficiently solved using methods such as interior point methods or a simplex method. 
     Alternately or additionally, Formula 2 may be simplified via a heuristic approach which decouples the estimation of the unlicensed spectrum rates, i.e., RU i,c   (n) , from the licensed spectrum rates, i.e., w i,c   (n) . 
       FIG. 3  is a flowchart of an example load estimation method  300 . The method  300  may begin with calculating the unlicensed spectrum rate at block  302 . The unlicensed spectrum rate may be represented by the variable RU i,c   (n)′ , which may be defined as in Formula 4. 
     
       
         
           
             
               
                 
                   
                     RU 
                     
                       i 
                       , 
                       c 
                     
                     
                       
                         ( 
                         n 
                         ) 
                       
                       ′ 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               min 
                               ⁢ 
                               
                                 { 
                                 
                                   
                                     
                                       
                                         
                                           r 
                                           _ 
                                         
                                         
                                           i 
                                           , 
                                           c 
                                         
                                         
                                           ( 
                                           n 
                                           ) 
                                         
                                       
                                       
                                         
                                           ∑ 
                                           
                                             l 
                                             ∈ 
                                             
                                               Ω 
                                               n 
                                               ′ 
                                             
                                           
                                         
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           
                                             ∑ 
                                             
                                               s 
                                               ∈ 
                                               
                                                 C 
                                                 l 
                                                 
                                                   ( 
                                                   n 
                                                   ) 
                                                 
                                               
                                             
                                           
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           
                                             
                                               r 
                                               _ 
                                             
                                             
                                               l 
                                               , 
                                               s 
                                             
                                             
                                               ( 
                                               n 
                                               ) 
                                             
                                           
                                         
                                       
                                     
                                     ⁢ 
                                     
                                       ( 
                                       
                                         
                                           
                                             
                                               
                                                 R 
                                                 AP 
                                                 
                                                   ( 
                                                   n 
                                                   ) 
                                                 
                                               
                                               - 
                                             
                                           
                                         
                                         
                                           
                                             
                                               
                                                 ∑ 
                                                 
                                                   j 
                                                   = 
                                                   1 
                                                 
                                                 
                                                   W 
                                                   n 
                                                 
                                               
                                               ⁢ 
                                               
                                                   
                                               
                                               ⁢ 
                                               
                                                 R 
                                                 
                                                   w 
                                                   , 
                                                   j 
                                                 
                                                 
                                                   ( 
                                                   n 
                                                   ) 
                                                 
                                               
                                             
                                           
                                         
                                       
                                       ) 
                                     
                                   
                                   , 
                                   
                                     
                                       r 
                                       _ 
                                     
                                     
                                       i 
                                       , 
                                       c 
                                     
                                     
                                       ( 
                                       n 
                                       ) 
                                     
                                   
                                 
                                 } 
                               
                             
                             , 
                           
                         
                         
                           
                             
                               if 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 PQ 
                                 
                                   i 
                                   , 
                                   c 
                                 
                                 
                                   ( 
                                   n 
                                   ) 
                                 
                               
                             
                             ≥ 
                             
                               PQ 
                               th 
                             
                           
                         
                       
                       
                         
                           
                             0 
                             , 
                           
                         
                         
                           otherwise 
                         
                       
                     
                   
                 
               
               
                 
                   FORMULA 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   4 
                 
               
             
           
         
       
     
     Variable PQ i,c   (n)  of Formula 4 represents a priority of a certain QCI for connection c of terminal i connected to base station n. Variable PQ th  represents a threshold that may be adjusted based on the unlicensed spectrum congestion experienced by the telecommunication system  200 . For example, when the telecommunication system  200  is experiencing relatively low traffic on the unlicensed spectrum, PQ th  may be lowered to encourage more communication over the unlicensed spectrum. Conversely, when the unlicensed spectrum becomes relatively congested, PQ th  may be raised to urge high-priority traffic to the licensed spectrum. When PQ i,c   (n)  is less than PQ th , communication may be restricted to the licensed spectrum. However, when PQ i,c   (n)  is greater than, or equal to PQ th , communication may occur over the licensed and unlicensed spectrum to achieve the minimum rate requirement for the corresponding connection and terminal. 
     The set Ω′ n  represents a set of terminals associated with base station n with QCI values greater than or equal to PQ th . The available unlicensed spectrum capacity, i.e., R AP   (n) −Σ j=1   W     n   R w,j   (n) , may be distributed among terminals proportional to the terminals&#39; requested rates, i.e.,  r   i,c   (n) . 
     The minimization operator may encourage fairness between terminals by avoiding assigning any of the terminals a rate higher than the terminals&#39; requested rate. However, in some instances, the unlicensed spectrum may still have excess capacity after the requested rates of the terminals in Ω′ n  have been satisfied. The excess capacity may be determined and distributed to the terminals. Thus, the excess capacity may be distributed to the terminals such that the terminals may be assigned a rate in excess of the terminals&#39; requested rate. In some embodiments, the excess unlicensed spectrum capacity, i.e., R excess  may be determined as disclosed in Formula 5. 
     
       
         
           
             
               
                 
                   
                     R 
                     excess 
                   
                   = 
                   
                     
                       R 
                       AP 
                       
                         ( 
                         n 
                         ) 
                       
                     
                     - 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           1 
                         
                         
                           W 
                           n 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         R 
                         
                           w 
                           , 
                           j 
                         
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                     - 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         
                           S 
                           n 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         RU 
                         
                           i 
                           , 
                           c 
                         
                         
                           
                             ( 
                             n 
                             ) 
                           
                           ′ 
                         
                       
                     
                   
                 
               
               
                 
                   FORMULA 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   5 
                 
               
             
           
         
       
     
     Furthermore, the terminals&#39; unlicensed spectrum rate, i.e., RU i,c   (n) *, may be adjusted to include the excess capacity as disclosed in Formula 6. 
     
       
         
           
             
               
                 
                   
                     RU 
                     
                       i 
                       , 
                       c 
                     
                     
                       
                         ( 
                         n 
                         ) 
                       
                       * 
                     
                   
                   = 
                   
                     
                       RU 
                       
                         i 
                         , 
                         c 
                       
                       
                         
                           ( 
                           n 
                           ) 
                         
                         ′ 
                       
                     
                     + 
                     
                       
                         
                           
                             r 
                             _ 
                           
                           
                             i 
                             , 
                             c 
                           
                           
                             ( 
                             n 
                             ) 
                           
                         
                         
                           
                             ∑ 
                             
                               l 
                               ∈ 
                               
                                 Ω 
                                 n 
                                 ′ 
                               
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             
                               ∑ 
                               
                                 s 
                                 ∈ 
                                 
                                   C 
                                   l 
                                   
                                     ( 
                                     n 
                                     ) 
                                   
                                 
                               
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               
                                 r 
                                 _ 
                               
                               
                                 l 
                                 , 
                                 s 
                               
                               
                                 ( 
                                 n 
                                 ) 
                               
                             
                           
                         
                       
                       ⁢ 
                       
                         R 
                         excess 
                       
                     
                   
                 
               
               
                 
                   FORMULA 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   6 
                 
               
             
           
         
       
     
     The method  300  continues at block  304 , where the licensed spectrum load is estimated. At block  306 , the licensed spectrum power is allocated. In some embodiments, the load estimation  304  and power allocation  306  may be performed as an iterative method, as indicated in block  308 . In some embodiments, the iterative method including blocks  304 - 308  may be based on the conventional concept of water-filling and may be performed as disclosed in Formulas 7, 8, and 9. 
     
       
         
           
             
               
                 
                   
                     
                       
                         w 
                         
                           i 
                           , 
                           c 
                         
                         
                           ( 
                           n 
                           ) 
                         
                       
                       ⁡ 
                       
                         ( 
                         
                           t 
                           + 
                           1 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         
                           
                             r 
                             _ 
                           
                           
                             i 
                             , 
                             c 
                           
                           
                             ( 
                             n 
                             ) 
                           
                         
                         - 
                         
                           RU 
                           
                             i 
                             , 
                             c 
                           
                           
                             
                               ( 
                               n 
                               ) 
                             
                             * 
                           
                         
                       
                       
                         
                           B 
                           K 
                         
                         ⁢ 
                         
                           
                             log 
                             2 
                           
                           ⁡ 
                           
                             ( 
                             
                               1 
                               + 
                               
                                 
                                   
                                     P 
                                     i 
                                     
                                       ( 
                                       n 
                                       ) 
                                     
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       t 
                                       + 
                                       1 
                                     
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   α 
                                   i 
                                   
                                     ( 
                                     n 
                                     ) 
                                   
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         w 
                         
                           i 
                           , 
                           c 
                         
                         
                           ( 
                           n 
                           ) 
                         
                       
                       ⁡ 
                       
                         ( 
                         0 
                         ) 
                       
                     
                     = 
                     
                       K 
                       
                         
                           ∑ 
                           
                             i 
                             ∈ 
                             
                               Ω 
                               n 
                               ″ 
                             
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                            
                           
                             C 
                             i 
                             
                               ( 
                               n 
                               ) 
                             
                           
                            
                         
                       
                     
                   
                 
               
               
                 
                   FORMULA 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   7 
                 
               
             
             
               
                 
                   
                     
                       λ 
                       i 
                       
                         ( 
                         n 
                         ) 
                       
                     
                     ⁡ 
                     
                       ( 
                       
                         t 
                         + 
                         1 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         ∑ 
                         
                           i 
                           ∈ 
                           
                             Ω 
                             n 
                             ″ 
                           
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           ∑ 
                           
                             c 
                             ∈ 
                             
                               C 
                               i 
                               
                                 ( 
                                 n 
                                 ) 
                               
                             
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             w 
                             
                               i 
                               , 
                               c 
                             
                             
                               ( 
                               n 
                               ) 
                             
                           
                           ⁡ 
                           
                             ( 
                             
                               t 
                               + 
                               1 
                             
                             ) 
                           
                         
                       
                     
                     
                       
                         P 
                         max 
                         
                           ( 
                           n 
                           ) 
                         
                       
                       + 
                       
                         
                           ∑ 
                           
                             i 
                             ∈ 
                             
                               Ω 
                               n 
                               ″ 
                             
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             
                               ∑ 
                               
                                 c 
                                 ∈ 
                                 
                                   C 
                                   i 
                                   
                                     ( 
                                     n 
                                     ) 
                                   
                                 
                               
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               
                                 w 
                                 
                                   i 
                                   , 
                                   c 
                                 
                                 
                                   ( 
                                   n 
                                   ) 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   t 
                                   + 
                                   1 
                                 
                                 ) 
                               
                             
                           
                           
                             α 
                             i 
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   FORMULA 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   8 
                 
               
             
             
               
                 
                   
                     
                       P 
                       i 
                       
                         ( 
                         n 
                         ) 
                       
                     
                     ⁡ 
                     
                       ( 
                       
                         t 
                         + 
                         1 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       ( 
                       
                         
                           1 
                           
                             
                               λ 
                               i 
                               
                                 ( 
                                 n 
                                 ) 
                               
                             
                             ⁡ 
                             
                               ( 
                               t 
                               ) 
                             
                           
                         
                         - 
                         
                           1 
                           
                             α 
                             i 
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                       
                       ) 
                     
                     + 
                   
                 
               
               
                 
                   FORMULA 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   9 
                 
               
             
           
         
       
     
     Variable t in Formulas 7, 8, and 9 represents an iteration index. Set Ω n ″ represents the set of terminals with minimum rate requirements that have not yet been fully satisfied in the unlicensed spectrum. 
     Parameter λ i   (n)  represents an intermediate parameter for water filling. Variable α i   (n)  is defined as 
               H   i     (   n   )         σ   2           
and represents the average SNR of the i th  terminal connected to base station n.
 
     Formulas 7-9 are performed iteratively until stopping criteria are met (“Yes” at block  308  of  FIG. 3 ). In some embodiments, the stopping criteria may be met when a maximum number of iterations is reached, or when w i,c   (n) (t) or P i   (n) (t) reach a steady state value. 
     With reference again to  FIG. 2 , the central controller  102  may perform interference management and licensed spectrum resource assignment for the base stations  104 . In some embodiments, the interference management and licensed spectrum resource assignment may be performed via graph coloring  206 . The graph coloring  206  may be based on the interference graph constructed at block  208 , as well as the output  207  of the load estimation  204  performed by each of the base stations  104  or at the central controller  102 . Based on the graph coloring, the central controller  102  may assign  210  licensed spectrum resources, i.e., a set of PRBs, to each of the base stations  104 . 
     Optimal graph coloring is a non-deterministic polynomial-time hard (“NP-hard”) problem conventionally solved using heuristics. In some embodiments, an iterative greedy algorithm as disclosed herein may be used. The iterative greedy algorithm may allow frequency reuse between base stations  104  where significant interference is not expected. As a result, the system capacity may be increased. To perform the iterative greedy algorithm, a conventional interference graph formula may be modified into a weighted interference graph where the weight of each directed edge, i.e. ρ nm , is given by Formula 10. 
     
       
         
           
             
               
                 
                   
                     ρ 
                     nm 
                   
                   = 
                   
                     
                       
                         P 
                         max 
                         
                           ( 
                           n 
                           ) 
                         
                       
                       
                         ℳ 
                         n 
                       
                     
                     ⁢ 
                     
                       G 
                       nm 
                     
                   
                 
               
               
                 
                   FORMULA 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   10 
                 
               
             
           
         
       
     
     Variable G nm  of Formula 10 represents an average path loss between base station n and base station m, which may be defined as an average path loss between base station n and the terminals associated with base station m. Alternately, G nm  may be defined as the path loss between base station n and a fictitious terminal located at base station m. 
     The value 
               P   max     (   n   )         ℳ   n           
represents the average power per PRB for base station n.
 
     Introducing weighting to the interference graph may promote the graph coloring scheme to be adaptive to the base stations&#39; demands in terms of requested load. For example, if the total requested load of all base stations  104  is less than or equal to the total number of available PRBs and/or channels in the system, i.e., if Σ n=1   N               n ≦K, then orthogonal frequency allocation may be provided by the graph coloring algorithm without mutual interference between base stations  104 . However, if the base stations  104  request more PRBs than are available in the telecommunication system  200 , the graph coloring algorithm disclosed herein may reuse frequencies of PRBs, i.e., colors, in a way that minimizes the interference seen by each of the base stations  104 , rather than assigning each of the base stations  104  fewer PRBs than requested.
       FIG. 4  is a flowchart of an example graph coloring method  400 . The graph coloring method  400  may employ frequency reuse. The method  400  may begin at block  402 , where an association table and a cost table may be initialized by setting all entries in the association and cost tables to 0. Furthermore, set V′, which represents the set of uncolored vertices in the constructed interference graph, is defined to be equal to V, which represents the set of all vertices in the constructed interference graph. As disclosed with reference to block  208  of  FIG. 2 , each vertex of the constructed interference graph may represent one of the base stations  104 . 
     The association table may be an N×J table with binary entries a nj . N may be the total number of base stations  104  and J may be the total number of colors. The parameter J may be set equal to K, i.e., one color may be denoted per each available PRB. Alternately, the parameter J may be set equal to K/v, i.e., one color may be denoted per v PRBs. A value of v greater than 1 may decrease the complexity of the graph coloring, but at the expense of creating a coarser and less flexible channel assignment. An entry a nj  in the association table may be set to 1 if base station n is assigned color j. Otherwise, the entry a nj  may be set to 0. 
     The cost table may be an N×J table with real-valued entries c nj  representing the cost of using color j for base station n. The cost may be defined as the sum of the interference powers from all other base stations  104  assigned the color j. An entry c nj  may be defined as disclosed in Formula 11. 
     
       
         
           
             
               
                 
                   
                     c 
                     nj 
                   
                   = 
                   
                     
                       ∑ 
                       
                         
                           m 
                           = 
                           1 
                         
                         
                           m 
                           ≠ 
                           n 
                         
                       
                       N 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         a 
                         mj 
                       
                       ⁢ 
                       
                         
                           P 
                           max 
                           
                             ( 
                             m 
                             ) 
                           
                         
                         
                           ℳ 
                           m 
                         
                       
                       ⁢ 
                       
                         G 
                         mn 
                       
                     
                   
                 
               
               
                 
                   FORMULA 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   11 
                 
               
             
           
         
       
     
     The method  400  may continue at block  404 , where a base station n′ causing the largest sum interference may be found. In some embodiments, this may include choosing the base station n′ with the largest sum of outgoing edge weights as disclosed in Formula 12. 
     
       
         
           
             
               
                 
                   
                     n 
                     ′ 
                   
                   = 
                   
                     
                       arg 
                       ⁢ 
                       
                         
                           max 
                           
                             n 
                             ∈ 
                             V 
                           
                         
                         ⁢ 
                         
                           
                             ∑ 
                             
                               
                                 m 
                                 = 
                                 1 
                               
                               
                                 m 
                                 ≠ 
                                 n 
                               
                             
                             N 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ρ 
                             nm 
                           
                         
                       
                     
                     = 
                     
                       arg 
                       ⁢ 
                       
                         
                           max 
                           
                             n 
                             ∈ 
                             V 
                           
                         
                         ⁢ 
                         
                           
                             
                               P 
                               max 
                               
                                 ( 
                                 n 
                                 ) 
                               
                             
                             
                               ℳ 
                               n 
                             
                           
                           ⁢ 
                           
                             
                               ∑ 
                               
                                 
                                   m 
                                   = 
                                   1 
                                 
                                 
                                   m 
                                   ≠ 
                                   n 
                                 
                               
                               N 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               G 
                               nm 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   FORMULA 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   12 
                 
               
             
           
         
       
     
     Choosing the base station causing the largest sum interference may be advantageous, as the chosen base station n′ may be considered to be the most troublesome of the base stations  104 . In some embodiments, if more than one base station n′ has the same largest sum of outgoing edge weights, the base station n′ with the largest              n  may be chosen.
     The method  400  may continue at block  406 , where              n′  colors with the lowest cost may be selected for the base station n′ chosen in block  404 . The colors may be determined as disclosed in Formula 13.
     
       
         
           
             
               
                 
                   
                     c 
                     
                       
                         n 
                         ′ 
                       
                       ⁢ 
                       j 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         
                           m 
                           = 
                           1 
                         
                         
                           m 
                           ≠ 
                           n 
                         
                       
                       N 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         a 
                         mj 
                       
                       ⁢ 
                       
                         
                           P 
                           max 
                           
                             ( 
                             m 
                             ) 
                           
                         
                         
                           ℳ 
                           m 
                         
                       
                       ⁢ 
                       
                         G 
                         
                           mn 
                           ′ 
                         
                       
                     
                   
                 
               
               
                 
                   FORMULA 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   13 
                 
               
             
           
         
       
     
     In some embodiments, if more than              n′  colors result in the same minimal cost, the colors that are most frequently used are chosen. The colors that are most frequently used may be identified from the association table. Selecting the colors that are most frequently used may provide less interference for subsequent base stations in the coloring process, as colors that are less frequently used generally have a higher probability of having a lower cost to the subsequent base stations.
     The method  400  may continue to block  408 , where the allocation table and cost table are updated. The allocation table and the cost table are generally updated to reflect the colors, i.e., PRBs, allocated to the base station n′ in block  406 . In block  410 , the set of uncolored vertices, V′, is updated by removing the vertex associated with the base station n′ from the set. 
     In block  412 , the set of uncolored vertices, V′, is checked to determine whether the set is empty. If V′ is empty, i.e., if all of the vertices are colored, the method  400  continues to block  414 . However, if V′ is not empty, i.e., if one or more vertices have not been colored yet, the method  400  returns to block  404 , where a new base station n′ is chosen and subsequently colored in block  406 . 
     At block  414 , it may be determined whether stopping criteria have been met. If the stopping criteria are met, the method  400  may continue to block  416 . If the stopping criteria are not met, the method  400  may continue to block  420 , where the set of uncolored vertices, V′, may be again defined as the set of all vertices V, and blocks  404 - 414  of the method  400  may be repeated. The iterative approach to the graph coloring introduced by blocks  414  and  420  may enhance the graph coloring method  400 . In some embodiments, because the method  400  performs coloring of vertices in a sequential manner, the effect of a colored base station is not taken into consideration in the cost of previously colored base stations, which may be mitigated by coloring base stations in a descending order of the amount of interference they cause in block  404 . This sequential behavior is enhanced by the iterative approach by repeating blocks  404 - 414 . Stopping criteria may include a maximum number of iterations, a steady state value for a reuse metric, or the like. The reuse metric may be defined as a total amount of mutual interference power caused by the base stations. 
     When the stopping criteria have been met in block  414 , the method  400  may continue to block  416 . At block  416 , any unused colors, i.e., unassigned PRBs, may be distributed to the base stations. In some embodiments, the unassigned PRBs may be distributed to each base station in an amount proportional to the sum of the requested rates of an individual base station&#39;s associated terminals over the requested rate of all base stations&#39; associated terminals. In some embodiments, the association table may then be updated to include the PRBs distributed at block  416 . 
     The method  400  may conclude at block  418  by assigning each base station the final set of PRBs, i.e.,              n , according to the association table. In some embodiments, each base station may also be provided with a set of interfering base stations on each PRB k and the average interference power from every interfering base station in the set of interfering base stations.
     Referring again to  FIG. 2 , the base station  104   a  may receive  210  a set of assigned PRBs as a result of method  400 . 
     The base station  104   a  may then perform resource and power allocation  212  for each terminal (not shown) assigned to the base station  104   a . The resource and power allocation  212  may include fine-tuning the resource allocation to each terminal and performing power allocation on a per-PRB basis for resources in the licensed spectrum. The resource and power allocation  212  may further include unlicensed spectrum resource allocation for the associated terminals. Resource allocation in both the licensed and unlicensed spectrums may be done jointly to satisfy the terminals&#39; data rate requirements and to achieve fairness between the terminals. 
     The central controller  102  may generally perform coarse-resolution resource allocation through graph coloring  206 , generally on a longer timescale than the base stations  104 . The resource allocation may be based on long-term interference management statistics provided by the base station measurements  209  and/or terminal reports  220 . The set of PRBs assigned  210  to each base station  104  may be assigned to achieve a trade-off between interference control between the base stations  104  and spectrum reuse to enhance the total system throughput. 
     In comparison, the base station  104   a  may perform fine-resolution resource allocation to the terminals  110  on both the licensed and unlicensed spectrums via the resource and power allocation  212 , generally on a shorter timescale than the central controller  102 . For example, in embodiments employing LTE-A, resource reallocation may be allowed every Transmission Time Interval (TTI), generally equal to 1 millisecond (ms). In some embodiments, the central controller  102  may perform graph coloring  206  and resource allocation on a timescale of hundreds of TTIs, whereas the base station  104   a  may perform resource allocation  212  every TTI or every few TTIs. 
     In some embodiments, to ensure fairness among terminals, the base station  104   a  performs licensed spectrum allocation, per-PRB power allocation, and unlicensed spectrum allocation at block  212  according to a max-min fairness criteria described in Formula 14. 
     
       
         
           
             
               
                 
                   
                     FORMULA 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     14 
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     max 
                     
                       { 
                       
                         
                           p 
                           
                             i 
                             , 
                             k 
                           
                           
                             ( 
                             n 
                             ) 
                           
                         
                         , 
                         
                           s 
                           
                             i 
                             , 
                             k 
                           
                           
                             ( 
                             n 
                             ) 
                           
                         
                         , 
                         
                           RU 
                           ic 
                         
                       
                       } 
                     
                   
                   ⁢ 
                   
                     
                       min 
                       i 
                     
                     ⁢ 
                     
                       
                         1 
                         
                           
                             ∑ 
                             
                               c 
                               ∈ 
                               
                                 C 
                                 i 
                                 
                                   ( 
                                   n 
                                   ) 
                                 
                               
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             
                               r 
                               _ 
                             
                             
                               i 
                               , 
                               c 
                             
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               B 
                               K 
                             
                             ⁢ 
                             
                               
                                 ∑ 
                                 
                                   k 
                                   ∈ 
                                   
                                     ℳ 
                                     n 
                                   
                                 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   s 
                                   
                                     i 
                                     , 
                                     k 
                                   
                                   
                                     ( 
                                     n 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     log 
                                     2 
                                   
                                   ( 
                                   
                                     1 
                                     + 
                                     
                                       
                                         
                                           p 
                                           
                                             i 
                                             , 
                                             k 
                                           
                                           
                                             ( 
                                             n 
                                             ) 
                                           
                                         
                                         ⁢ 
                                         
                                           h 
                                           
                                             i 
                                             , 
                                             k 
                                           
                                           
                                             ( 
                                             n 
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           s 
                                           
                                             i 
                                             , 
                                             k 
                                           
                                           
                                             ( 
                                             n 
                                             ) 
                                           
                                         
                                         ( 
                                         
                                           
                                             σ 
                                             2 
                                           
                                           + 
                                           
                                             
                                               ∑ 
                                               
                                                 j 
                                                 ∈ 
                                                 
                                                   I 
                                                   k 
                                                 
                                               
                                             
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             
                                               P 
                                               k 
                                               
                                                 ( 
                                                 jn 
                                                 ) 
                                               
                                             
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           + 
                           
                             
                               ∑ 
                               
                                 c 
                                 ∈ 
                                 
                                   C 
                                   i 
                                   
                                     ( 
                                     n 
                                     ) 
                                   
                                 
                               
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               RU 
                               
                                 i 
                                 , 
                                 c 
                               
                               
                                 ( 
                                 n 
                                 ) 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   14 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   a 
                 
               
             
             
               
                 
                   
                     subject 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     to 
                     ⁢ 
                     
                       : 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           k 
                           ∈ 
                           
                             ℳ 
                             n 
                           
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           ∑ 
                           
                             i 
                             ∈ 
                             
                               Ω 
                               n 
                             
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           p 
                           
                             i 
                             , 
                             k 
                           
                           
                             ( 
                             n 
                             ) 
                           
                         
                       
                     
                   
                   ≤ 
                   
                     P 
                     max 
                     
                       ( 
                       n 
                       ) 
                     
                   
                 
               
               
                 
                   14 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   b 
                 
               
             
             
               
                 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       
                         S 
                         n 
                       
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         ∑ 
                         
                           c 
                           ∈ 
                           
                             C 
                             i 
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         RU 
                         
                           i 
                           , 
                           c 
                         
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                   
                   ≤ 
                   
                     
                       R 
                       AP 
                       
                         ( 
                         n 
                         ) 
                       
                     
                     - 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           1 
                         
                         
                           W 
                           n 
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         R 
                         
                           w 
                           , 
                           j 
                         
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   14 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   c 
                 
               
             
             
               
                 
                   
                     
                       
                         ∑ 
                         
                           i 
                           ∈ 
                           
                             Ω 
                             n 
                           
                         
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         s 
                         
                           i 
                           , 
                           k 
                         
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                     = 
                     1 
                   
                   , 
                   
                     ∀ 
                     
                       k 
                       ∈ 
                       
                         ℳ 
                         n 
                       
                     
                   
                 
               
               
                 
                   14 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   d 
                 
               
             
             
               
                 
                   
                     
                       s 
                       
                         i 
                         , 
                         k 
                       
                       
                         ( 
                         n 
                         ) 
                       
                     
                     ≥ 
                     0 
                   
                   , 
                   
                     
                       p 
                       
                         i 
                         , 
                         k 
                       
                       
                         ( 
                         n 
                         ) 
                       
                     
                     ≥ 
                     0 
                   
                   , 
                   
                     ∀ 
                     
                       i 
                       ∈ 
                       
                         Ω 
                         n 
                       
                     
                   
                   , 
                   
                     ∀ 
                     
                       k 
                       ∈ 
                       
                         ℳ 
                         n 
                       
                     
                   
                 
               
               
                 
                   14 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   e 
                 
               
             
             
               
                 
                   
                     0 
                     ≤ 
                     
                       RU 
                       
                         i 
                         , 
                         c 
                       
                       
                         ( 
                         n 
                         ) 
                       
                     
                     ≤ 
                     
                       RU 
                       
                         i 
                         , 
                         c 
                         , 
                         max 
                       
                       
                         ( 
                         n 
                         ) 
                       
                     
                   
                   , 
                   
                     ∀ 
                     
                       i 
                       ∈ 
                       
                         Ω 
                         n 
                       
                     
                   
                   , 
                   
                     ∀ 
                     
                       c 
                       ∈ 
                       
                         C 
                         i 
                         
                           ( 
                           n 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   14 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   f 
                 
               
             
           
         
       
     
     Formula 14 may generally maximize the worst ratio of achieved rate to requested rate for all terminals associated with base station n. As seen in subformula 14a, the achieved rate may be obtained over the licensed spectrum, the unlicensed spectrum, or both. The requested rate for a particular terminal may be defined as the sum of the requested rates for all of the connections of the particular terminal. 
     In Formula 14, set I k  represents a set of interfering base stations on each PRB k. Variable P k   (jn)  represents the average interference power from every interfering base station j in the set I k  to base station n on PRB k. Variable s i,k   (n)  represents the time-sharing coefficient of PRB k for terminal i in base station n. In some embodiments, base station n may allocate a fraction of PRBs to the terminals. For example, one or more terminals may be allocated a PRB k for a fraction of time. 
     Subformula 14b ensures the sum of the per-PRB power over all PRBs in set              n  and over all terminals associated with base station n is limited to the base station n&#39;s maximum transmission power.
     Subformula 14c ensures the sum of the unlicensed spectrum rates assigned to the terminals of base station n is upper-bounded by the available unlicensed spectrum capacity at base station n. 
     Subformula 14d ensures that the sum of all time shares of a PRB k is equal to 1. 
     Subformulas 14e and 14f define the ranges of s i,k   (n) , p i,k   (n) , and RU i,c   (n) . In some embodiments, the distribution of the licensed spectrum resources, i.e., s i,k   (n) , for each terminal i among the connections c requested by the terminal may be accomplished in a fine-resolution scheduling step in an optional licensed spectrum scheduler  218  of the base station  104   a . The distribution of the licensed spectrum resources may depend on the requested rate of each connection, i.e.,  r   i,c   (n) , as well as the assigned unlicensed spectrum rate for each connection, i.e., RU i,c   (n) , as calculated by Formula 14. 
     Advantageously, Formula 14 is a convex optimization problem that may be solved efficiently and in an easy manner. However, in some embodiments, Formula 14 may be simplified. For example, 
               p     i   ,   k       (   n   )         s     i   ,   k       (   n   )             
may be approximated as
 
                 P   i     (   n   )           ∑     c   ∈     C   i     (   n   )           ⁢           ⁢     w     i   ,   c       (   n   )           ,         
where P i   (n)  and Σ cεC     i       (n)   w i,c   (n)  are obtained at the load estimation  204 .
 
     Alternately or additionally, Formula 14 may be simplified by decoupling the resource allocation over the licensed and unlicensed spectrums, similar to the decoupling simplification described with reference to Formula 2. Decoupling the resource allocation over the licensed and unlicensed spectrums may lead to a simplified problem as disclosed in Formula 15. Advantageously, Formula 15 is a linear programming problem that may be computationally easier to solve than Formula 14. 
     
       
         
           
             
               
                 
                   
                     FORMULA 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     15 
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     max 
                     
                       s 
                       
                         i 
                         , 
                         k 
                       
                       
                         ( 
                         n 
                         ) 
                       
                     
                   
                   ⁢ 
                   
                     
                       min 
                       i 
                     
                     ⁢ 
                     
                       
                         1 
                         
                           
                             ∑ 
                             
                               c 
                               ∈ 
                               
                                 C 
                                 i 
                                 
                                   ( 
                                   n 
                                   ) 
                                 
                               
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             
                               r 
                               _ 
                             
                             
                               i 
                               , 
                               c 
                             
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               B 
                               K 
                             
                             ⁢ 
                             
                               
                                 ∑ 
                                 
                                   k 
                                   ∈ 
                                   
                                     ℳ 
                                     n 
                                   
                                 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   s 
                                   
                                     i 
                                     , 
                                     k 
                                   
                                   
                                     ( 
                                     n 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     log 
                                     2 
                                   
                                   ( 
                                   
                                     1 
                                     + 
                                     
                                       
                                         
                                           P 
                                           i 
                                           
                                             ( 
                                             n 
                                             ) 
                                           
                                         
                                         ⁢ 
                                         
                                           h 
                                           
                                             i 
                                             , 
                                             k 
                                           
                                           
                                             ( 
                                             n 
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           ∑ 
                                           
                                             c 
                                             ∈ 
                                             
                                               C 
                                               i 
                                               
                                                 ( 
                                                 n 
                                                 ) 
                                               
                                             
                                           
                                         
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           
                                             w 
                                             
                                               i 
                                               , 
                                               c 
                                             
                                             
                                               ( 
                                               n 
                                               ) 
                                             
                                           
                                           ( 
                                           
                                             
                                               σ 
                                               2 
                                             
                                             + 
                                             
                                               
                                                 ∑ 
                                                 
                                                   j 
                                                   ∈ 
                                                   
                                                     I 
                                                     k 
                                                   
                                                 
                                               
                                               ⁢ 
                                               
                                                   
                                               
                                               ⁢ 
                                               
                                                 P 
                                                 k 
                                                 
                                                   ( 
                                                   jn 
                                                   ) 
                                                 
                                               
                                             
                                           
                                           ) 
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           + 
                           
                             
                               ∑ 
                               
                                 c 
                                 ∈ 
                                 
                                   C 
                                   i 
                                   
                                     ( 
                                     n 
                                     ) 
                                   
                                 
                               
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               RU 
                               
                                 i 
                                 , 
                                 c 
                               
                               
                                 
                                   ( 
                                   n 
                                   ) 
                                 
                                 * 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   15 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   a 
                 
               
             
             
               
                 
                   
                     
                       subject 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       to 
                       ⁢ 
                       
                         : 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           ∑ 
                           
                             i 
                             ∈ 
                             
                               Ω 
                               n 
                             
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           s 
                           
                             i 
                             , 
                             k 
                           
                           
                             ( 
                             n 
                             ) 
                           
                         
                       
                     
                     = 
                     1 
                   
                   , 
                   
                     ∀ 
                     
                       k 
                       ∈ 
                       
                         ℳ 
                         n 
                       
                     
                   
                 
               
               
                 
                   15 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   b 
                 
               
             
             
               
                 
                   
                     
                       s 
                       
                         i 
                         , 
                         k 
                       
                       
                         ( 
                         n 
                         ) 
                       
                     
                     ≥ 
                     0 
                   
                   , 
                   
                     ∀ 
                     
                       i 
                       ∈ 
                       
                         Ω 
                         n 
                       
                     
                   
                   , 
                   
                     ∀ 
                     
                       k 
                       ∈ 
                       
                         ℳ 
                         n 
                       
                     
                   
                 
               
               
                 
                   15 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   c 
                 
               
             
           
         
       
     
     Formula 14 and Formula 15 may employ the average interference information sent from the central controller  102  to the base stations  104 . Advantageously, the average interference information may result in an achieved rate from the respective optimization problem that is relatively close to the actual achieved rate. However, in some embodiments, the average interference information may not be sent by the central controller  102  to the base stations  104  such that the communication overheads between the central controller  102  and the base stations  104  are reduced. 
     In some embodiments, the SNR—as opposed to the SINR—may be considered. When the SNR is considered, the central controller  102  may send only the set of allocated PRBs to the base stations  104 , reducing the communication overheads between the central controller  102  and the base stations  104 . However, performance may be degraded, particularly where the average requested rate of all terminals is relatively high and the interference is large enough that it may be detrimental to ignore. 
     In embodiments where the interference is ignored, the optimization problem may be formulated as in Formula 14, but with the interference term, i.e., Σ jεI     k   P k   (jn) , omitted. The resulting formula may be further simplified in a manner similar to Formula 15, as disclosed in Formula 16. Advantageously, Formula 16 is a linear programming problem that may be computationally easier to solve than Formula 14. 
     
       
         
           
             
               
                 
                   
                     FORMULA 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     16 
                   
                   ⁢ 
                   
                       
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     max 
                     
                       s 
                       
                         i 
                         , 
                         k 
                       
                       
                         ( 
                         n 
                         ) 
                       
                     
                   
                   ⁢ 
                   
                     
                       min 
                       i 
                     
                     ⁢ 
                     
                       
                         1 
                         
                           
                             ∑ 
                             
                               c 
                               ∈ 
                               
                                 C 
                                 i 
                                 
                                   ( 
                                   n 
                                   ) 
                                 
                               
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             
                               r 
                               _ 
                             
                             
                               i 
                               , 
                               c 
                             
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               B 
                               K 
                             
                             ⁢ 
                             
                               
                                 ∑ 
                                 
                                   k 
                                   ∈ 
                                   
                                     ℳ 
                                     n 
                                   
                                 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   s 
                                   
                                     i 
                                     , 
                                     k 
                                   
                                   
                                     ( 
                                     n 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     log 
                                     2 
                                   
                                   ( 
                                   
                                     1 
                                     + 
                                     
                                       
                                         
                                           p 
                                           
                                             i 
                                             , 
                                             k 
                                           
                                           
                                             ( 
                                             n 
                                             ) 
                                           
                                         
                                         ⁢ 
                                         
                                           h 
                                           
                                             i 
                                             , 
                                             k 
                                           
                                           
                                             ( 
                                             n 
                                             ) 
                                           
                                         
                                       
                                       
                                         
                                           ∑ 
                                           
                                             c 
                                             ∈ 
                                             
                                               C 
                                               i 
                                               
                                                 ( 
                                                 n 
                                                 ) 
                                               
                                             
                                           
                                         
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           
                                             w 
                                             
                                               i 
                                               , 
                                               c 
                                             
                                             
                                               ( 
                                               n 
                                               ) 
                                             
                                           
                                           ⁢ 
                                           
                                             σ 
                                             2 
                                           
                                         
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                           
                           + 
                           
                             
                               ∑ 
                               
                                 c 
                                 ∈ 
                                 
                                   C 
                                   i 
                                   
                                     ( 
                                     n 
                                     ) 
                                   
                                 
                               
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               RU 
                               
                                 i 
                                 , 
                                 c 
                               
                               
                                 ( 
                                 n 
                                 ) 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   12 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     a 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     
                       subject 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       to 
                       ⁢ 
                       
                         : 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           ∑ 
                           
                             i 
                             ∈ 
                             
                               Ω 
                               n 
                             
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           s 
                           
                             i 
                             , 
                             k 
                           
                           
                             ( 
                             n 
                             ) 
                           
                         
                       
                     
                     = 
                     1 
                   
                   , 
                   
                     ∀ 
                     
                       k 
                       ∈ 
                       
                         ℳ 
                         n 
                       
                     
                   
                 
               
               
                 
                   12 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     b 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     
                       s 
                       
                         i 
                         , 
                         k 
                       
                       
                         ( 
                         n 
                         ) 
                       
                     
                     ≥ 
                     0 
                   
                   , 
                   
                     ∀ 
                     
                       i 
                       ∈ 
                       
                         Ω 
                         n 
                       
                     
                   
                   , 
                   
                     ∀ 
                     
                       k 
                       ∈ 
                       
                         ℳ 
                         n 
                       
                     
                   
                 
               
               
                 
                   12 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     c 
                     ) 
                   
                 
               
             
           
         
       
     
     Upon determining the resource and power distribution in block  212 , the base station  104   a  may perform packet distribution  214 . The optimization variables w i,c   (n)  and RU i,c   (n)  provided for each connection c and terminal i from the resource and power distribution  212  are generally sent to the packet distribution  214 . The packet distribution  214  may accordingly divide the downlink packets to the terminals over the licensed and unlicensed spectrums. 
     Given the number of PRBs assigned to each terminal and the duration of the resource allocation, denoted by T d , the packet distribution  214  may calculate the number of bits to send over the licensed spectrum in the duration T d . Furthermore, the packet distribution  214  may use the unlicensed spectrum downlink rate to the terminals, i.e., RU i,c   (n) , to calculate the number of bits to send over the unlicensed spectrum in the duration T d . 
     Given the number of bits to send over the licensed and unlicensed spectrums, a simple packet scheduling technique may be applied to divide packets between the licensed and unlicensed spectrums. For example, the packet distribution  214  may include a pair of virtual buckets for each terminal. The buckets may generally correspond to buckets used in conventional token bucket data rate monitoring techniques. One bucket may be associated with the licensed spectrum and the other bucket may be associated with the unlicensed spectrum. Upon receiving a downlink packet for terminal i, the packet distribution  214  may assign the packet to the licensed and/or unlicensed spectrums proportionally based on the ratio of the licensed spectrum rate, the unlicensed spectrum rate, and the accumulated number of bits transmitted over the spectrums as tracked by the buckets. In some embodiments, the buckets may reset at the beginning of the duration T d . For example, the buckets may reset such that the buckets are empty at the beginning of the duration T d . 
     An unlicensed spectrum scheduler  216  may receive packets from the packet distribution  214 , as well as packets to devices (not shown) generally corresponding to the devices  112  as described with reference to  FIG. 1 . The unlicensed spectrum scheduler  216  may multiplex the packets for contention on the unlicensed spectrum. The unlicensed spectrum scheduler  216  may provide information  222  about the unlicensed spectrum to the resource and power allocation  212 . For example, if the unlicensed spectrum scheduler experiences a large busy period, the provided information  222  may cause the resource and power allocation  212  to decrease the unlicensed spectrum traffic via one or more formulas described herein or by some other method. 
     An optional licensed spectrum scheduler  218  may manage additional scheduling requirements. For example, in embodiments employing LTE, the licensed spectrum scheduler  218  may accommodate hybrid automatic repeat request (HARQ) error correction scheduling. In other embodiments, the licensed spectrum scheduling  218  may accommodate other error checking and/or scheduling features. 
     The licensed spectrum scheduler  218  may receive packets from the packet distribution  214  and may apply conventional licensed spectrum scheduling mechanisms. For example, the licensed spectrum scheduler  218  may schedule downlink packets according to scheduling mechanisms that take into account the varying nature of the channel, uplink CQI reports of terminals, and/or acknowledgement (ACK) or negative acknowledgement (NAK) feedback from the terminals. 
     The licensed spectrum scheduler  218  may run more frequently than the resource and power allocation  212  to promote a better scheduling resolution more adaptive to channel conditions. 
       FIG. 5  is a flowchart of an example method  500  of controlling radio resources. The method  500  may be performed, in some embodiments, by a base station, such as the base stations  104  of  FIG. 1 . The method may begin at block  502  by communicating with multiple terminals via a licensed radio spectrum. The terminals may generally correspond to the terminals  110  described with reference to  FIG. 1 . The licensed radio spectrum may generally correspond to the licensed spectrum described with reference to  FIG. 1 . Communication with the multiple terminals via the licensed radio spectrum may include uplink and/or downlink communication. 
     The method  500  may continue at block  504  and may include communicating with the multiple terminals via an unlicensed radio spectrum. The unlicensed radio spectrum may generally correspond to the unlicensed spectrum described with reference to  FIG. 1 . Communication with the multiple terminals via the unlicensed radio spectrum may include uplink and/or downlink communication. 
     The method  500  may continue at block  506  and may include receiving from a central controller a licensed radio spectrum assignment including a set of assigned physical resource blocks associated with the licensed radio spectrum. The central controller may generally correspond to the central controller  102  described with reference to  FIGS. 1 and 2 . The assigned physical resource blocks may generally correspond to the assigned set of PRBs, i.e.              n , as described with reference to  FIG. 2 .
     The method  500  may continue at block  508  and may include allocating unlicensed radio spectrum resources and the licensed spectrum physical resource blocks among the multiple terminals. Allocating unlicensed radio spectrum resources and the licensed spectrum physical resource blocks among the multiple terminals may generally correspond to the resource and power allocation  212  as described with reference to  FIG. 2 . 
     In some embodiments, the method  500  may further include estimating radio resources desired by the multiple terminals for both the licensed radio spectrum and the unlicensed radio spectrum. Estimating radio resources desired by the multiple terminals for both the licensed radio spectrum and the unlicensed radio spectrum may generally correspond to the load estimation  204  as described with reference to  FIG. 2 . In some embodiments, the radio resources desired by the multiple terminals for both the licensed radio spectrum and the unlicensed radio spectrum may be estimated at least in part by decoupling an estimation of unlicensed radio spectrum rates from licensed radio spectrum rates. In some embodiments, the radio resources desired by the multiple terminals for both the licensed radio spectrum and the unlicensed radio spectrum are estimated at least in part by determining a minimum number of physical resource blocks that satisfy rate requirements of the plurality of terminals. 
     Furthermore, the method  500  may also include transmitting to the central controller the estimated radio resources desired by the multiple terminals for the licensed radio spectrum. Transmitting to the central controller the estimated radio resources desired by the multiple terminals for the licensed radio spectrum may generally correspond to outputting the load estimation  207  to the central controller  102  as described with reference to  FIG. 2 . 
     In some embodiments, the method  500  may further include distributing packets to be communicated to a terminal of the multiple terminals between the licensed radio spectrum and the unlicensed radio spectrum. Distributing the packets may generally correspond to the packet distribution  214  as described with reference to  FIG. 2 . In some embodiments, the packets to be communicated via the unlicensed radio spectrum are distributed to an unlicensed spectrum scheduler and the packets to be communicated via the licensed radio spectrum are distributed to a licensed spectrum scheduler. The unlicensed spectrum scheduler and the licensed spectrum scheduler may generally, respectively correspond to the unlicensed spectrum scheduler  216  and the licensed spectrum scheduler  218  described with reference to  FIG. 2 . 
     The embodiments described herein may include the use of a special purpose or general-purpose computer including various computer hardware or software modules, as discussed in greater detail below. 
     Embodiments described herein may be implemented using computer-readable media for carrying or having computer-executable instructions or data structures stored thereon. Such computer-readable media may be any available media that may be accessed by a general purpose or special purpose computer. By way of example, and not limitation, such computer-readable media may include non-transitory computer-readable storage media including Random Access Memory (RAM), Read-Only Memory (ROM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Compact Disc Read-Only Memory (CD-ROM) or other optical disk storage, magnetic disk storage or other magnetic storage devices, flash memory devices (e.g., solid state memory devices), or any other storage medium which may be used to carry or store desired program code in the form of computer-executable instructions or data structures and which may be accessed by a general purpose or special purpose computer. Combinations of the above may also be included within the scope of computer-readable media. 
     Computer-executable instructions comprise, for example, instructions and data which cause a general purpose computer, special purpose computer, or special purpose processing device to perform a certain function or group of functions. Although the subject matter has been described in language specific to structural features and/or methodological acts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or acts described above. Rather, the specific features and acts described above are disclosed as example forms of implementing the claims. 
     As used herein, the term “module” or “component” may refer to software objects or routines that execute on the computing system. The different components, modules, engines, and services described herein may be implemented as objects or processes that execute on the computing system (e.g., as separate threads). While some of the system and methods described herein are described as being implemented in software, implementations in hardware or a combination of software and hardware are also possible and contemplated. In this description, a “computing entity” may be any computing system as previously defined herein, or any module or combination of modulates running on a computing system. 
     All examples and conditional language recited herein are intended for pedagogical objects to aid the reader in understanding the invention and the concepts contributed by the inventor to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions. Although embodiments of the present inventions have been described in detail, it should be understood that the various changes, substitutions, and alterations could be made hereto without departing from the spirit and scope of the invention.