Patent Publication Number: US-2015078260-A1

Title: Parallel resource management in white space bands using transmit power control and channel set assignment

Description:
BACKGROUND 
     1. Field of the Disclosure 
     This disclosure relates generally to communication networks and, in particular, to parallel resource management in white space bands using transmit power control and channel assignment. 
     2. Description of the Related Art 
     As the number and types of wireless networks proliferate, and the amount of communication carried thereon increases, it has become increasingly desirable to manage networks comprising wireless networks of differing wireless access technologies, power limitations, frequency limitations, and other differences. Management of such heterogeneous networks may become increasingly complicated because of the shared nature of white space bands. While some solutions have been offered for managing coexistence in white space bands, maximization of spectrum re-use as well as spectrum utilization while avoiding interference remains a challenge. 
     SUMMARY 
     In one aspect, a disclosed method for parallel resource management in white space bands includes receiving location information for N wireless networks sharing K channels in white space bands having L permissible power levels, where N, K, and L are integers greater than 1. The method may include generating, for each of the L power levels, an interference graph of the N wireless networks, the interference graph comprising nodes each corresponding to a wireless network and edges each corresponding to interference between two nodes. A number of edges at each node may represent a node degree. The method may include initializing channel sets corresponding to the L power levels, beginning with channels having maximum power levels. The method may further include initializing network sets corresponding to the L power levels, including maximizing a number of networks in a maximum power network set corresponding to a maximum power level, and emptying network sets other than the maximum power network set. The method may also include updating the channel sets and network sets. A number of channels in a channel set corresponding to a network set may be greater than a maximum node degree of the interference graph for a corresponding power level. 
     Additional disclosed aspects for parallel resource management in white space bands include an article of manufacture comprising a non-transitory, computer-readable medium, and computer executable instructions stored on the computer-readable medium. A further aspect includes a management system for parallel resource management in white space bands comprising a memory, a processor coupled to the memory, a network interface, and computer executable instructions stored on the memory. 
     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. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the present invention and its advantages, reference is now made to the following description, taken in conjunction with the accompanying drawings, in which: 
         FIG. 1  is a block diagram of selected elements of an embodiment of a network for parallel resource management in white space bands; 
         FIG. 2  is a block diagram of selected elements of an embodiment of a management system for parallel resource management in white space bands; 
         FIGS. 3A ,  3 B, and  3 C show selected elements of embodiments of interference graphs; 
         FIG. 4  is a flow chart of selected elements of an embodiment of a method for parallel resource management in white space bands; 
         FIG. 5  is a flow chart of selected elements of an embodiment of a method for parallel resource management in white space bands; and 
         FIGS. 6A and 6B  show selected elements of embodiments of interference graphs. 
     
    
    
     DESCRIPTION OF PARTICULAR EMBODIMENT(S) 
     Wireless network providers are demanding more spectra to meet unprecedented growth in mobile data traffic. Despite this fact, the spectrum allocated in many bands (e.g. TV bands or federally allocated bands) may remain heavily underutilized. Regulatory entities around the world have been developing policies to enable access to the unused portions of the band (referred to as “white space bands”) when incumbents are not present. At a given location, channels in white space bands may be available for unlicensed access using different power levels, for example, depending on the proximity of incumbents. In order to exploit the additional resource provided by white space bands, multiple networks that share this spectra may be deployed, which may represent a valuable opportunity for wireless network providers. 
     However, without coordination of access to the white space bands, networks located in close proximity of each other may interfere, thus leading to poor performance. In addition, governed by white space regulations, each network may be allowed to transmit with only one transmit power level, regardless of the number of channels assigned. 
     As will be described in further detail herein, computational methods (e.g., algorithms) having polynomial-time complexity for heterogeneous coexistence management in white space bands have been developed. The computational methods presented herein may enable coordination of spectrum allocation and power levels such that harmful interference among neighboring networks is avoided, while utilization of individual channels in the white space bands is maximized. The computational methods described herein may split the networks and available white space band channels into disjoint sets with the objective of increasing spectrum re-use and utilization of channels with larger power levels. The disjoint sets may correspond to specific permissible power levels. Then, a channel assignment is performed in parallel for each network set from its corresponding channel set. 
     In the following description, details are set forth by way of example to facilitate discussion of the disclosed subject matter. It should be apparent to a person of ordinary skill in the field, however, that the disclosed embodiments are exemplary and not exhaustive of all possible embodiments. 
     Particular embodiments and their advantages are best understood by reference to  FIGS. 1 through 6 , wherein like numbers are used to indicate like and corresponding parts. 
     Turning now to the drawings,  FIG. 1  is a block diagram showing selected elements of an embodiment of network  100  for managing coexistence in white space bands, in accordance with certain embodiments of the present disclosure. In some embodiments, network  100  may include wireless networks  102 , user equipment  104 , and management system  200  communicatively coupled to wireless networks  102 . As shown in  FIG. 1 , management system  200  may be in fixed communication with wireless networks  102  using galvanic and/or optical media (not shown), for example. Wireless networks  102  may, in turn, provide wireless signals for enabling network access by user equipment  104  to allow communication by user equipment  104  across wireless networks  102 . As will be described herein, management system  200  may be configured to manage resources (e.g., channel assignments and/or power levels) to enable each of wireless networks  102  to operate in parallel while utilizing white space bands. 
     In some embodiments, wireless network  102  may be an access point to a communication network, the access point configured to allow user equipment  102  to communicate over the communication network. In some embodiments, each wireless network  102  shares substantially the same spectrum band as other wireless networks  102 , while potentially operating on a different wireless access technology (e.g., IEEE 802.11, IEEE 802.22, LTE, etc.). Further, each wireless network  102  may be owned and/or operated by a different operator. For example, system  100  may include four wireless networks  102 , including two LTE transmission towers, and two 802.22 wireless access points. In the same or alternative configurations, system  100  may include, more, fewer, or different configurations of wireless networks  102  without departing from the scope of the present disclosure. 
     In some embodiments, user equipment  104  may be an electronic device and/or combination of electronic devices configured to communicate and/or facilitate communication over any or all of the wireless networks  102 . For example, user equipment  104  may be a cellular telephone, tablet computer, laptop computer, network of other user equipment  104 , and/or other appropriate electronic device may be configured to transmit and/or receive data over wireless network  102 . 
     In operation of network  100 , white space bands may provide additional resources for wireless networks  102  to meet the increasing demand for mobile data traffic. Because of the scarcity of the spectrum and growing interest in offloading data traffic over white space bands, management system  200  may be enabled to control interference among neighbor networks and to increase resource (i.e., channel and/or power) utilization. White space bands may provide additional spectra with different power levels (e.g., in the TV band) for some channels depending on the activity of incumbents. In order to reuse spectrum and to better utilize additional power levels on some channels, orthogonal channel assignment may be provided along with power control, subject to regulatory constraints. 
     In certain cases where a number of available channels is constrained to a few channels, orthogonal sharing in time domain may be solved using a linear algorithm that may be efficiently solved. In situations where time sharing is not feasible, the complexity of the corresponding integer optimization problem may grow exponentially with the number of networks, available channels, and/or power levels and may result in a computationally intractable problem. Such a solution would need to assign channel(s) with a certain power level to a subset of networks. However, as given by current white space regulations, a network may only transmit with one power level when operating in white space bands, regardless of the number of channels used, which may result in spectral inefficiency and poor utilization of available channels. 
     As disclosed herein, an algorithm for parallel resource management in white space bands may generate disjoint sets of networks and channels using heuristics aimed at increasing overall resource utilization. The algorithm(s) disclosed herein may have polynomial-time complexity and may thus be solved efficiently. The channels in each channel set, which represents a permissible power level, may be allocated to the networks in the corresponding network set. Furthermore, these sets may be constructed such that a cardinality of a channel set is greater than a maximum node degree of an interference graph for a corresponding network set. Then, various channel assignment algorithms may be used in parallel for each network-channel set to allocate specific channels to networks. Hence, the algorithm disclosed herein may achieve a joint power control and channel assignment solution in polynomial-time complexity. 
     Referring now to  FIG. 2 , a block diagram illustrates selected elements of an embodiment of management system  200  for parallel white space resource management according to the present disclosure. In the embodiment depicted in  FIG. 2 , management system  200  includes processor  201  coupled via shared bus  202  to storage media collectively identified as memory media  210 . Management system  200 , as depicted in  FIG. 2 , further includes network adapter  220  that interfaces management system  200  to a network, such as portions of network  100 , including wireless networks  102  (see  FIG. 1 ). 
     In  FIG. 2 , memory media  210  may comprise persistent and volatile media, fixed and removable media, and magnetic and semiconductor media. Memory media  210  is operable to store instructions, data, or both. Memory media  210  as shown includes sets or sequences of instructions  224 , namely, an operating system  212  and parallel resource management  214 . Operating system  212  may be a UNIX or UNIX-like operating system, a Windows® family operating system, or another suitable operating system. Instructions  224  may also reside, completely or at least partially, within processor  201  during execution thereof. It is further noted that processor  201  may be configured to receive instructions  224  from memory media  210  via shared bus  202 . As described herein, parallel resource management  214  may represent instructions and/or code for implementing various algorithms according to the present disclosure. 
     Turning now to  FIGS. 3A-3C , a system model for an area where N networks share K white space channels for L permissible power levels is illustrated in the form of interference graphs  300 ,  301 , and  302 , where N=4 and L=3. In  FIGS. 3A ,  3 B, and  3 C, respective interference graphs  300 ,  301 , and  302  may each represent a network topology at a different power level. In interference graphs  300 ,  301 , and  302 , the network nodes (circles) represent different networks and edges between nodes (lines) are present when two networks interfere with one another. In one interference graph, it is assumed that all network nodes transmit at substantially the same power level. In  FIGS. 3A-3C , an exemplary embodiment of four network nodes  310 ,  312 ,  314 , and  316  is shown for descriptive clarity. It will be understood that, in different embodiments, interference graphs, as described herein, may have different numbers of network nodes and edges. 
     In interference graph  300  of  FIG. 3A , network node  310  may interfere with network nodes  312  and  314 , while network node  312  also interferes with network node  316 . In interference graph  301  of  FIG. 3B , all the edges in interference graph  300  are present, with network node  314  additionally interfering with network node  312 . In interference graph  302  of  FIG. 3C , all the edges in interference graph  301  are present, with network node  316  additionally interfering with network nodes  310  and  314 . As shown in  FIGS. 3A-3C , the power level increases from a first power level for interference graph  300  to a second power level for interference graph  301  to a third power level for interference graph  302 . Thus, for larger power levels, the interference graph may become denser and may indicate fewer opportunities for spectrum re-use. 
     In each of interference graphs  300 ,  301 , and  302 , a “node degree” may be defined as a number of edges per network node. Accordingly, the node degrees for interference graphs  300 ,  301 , and  302  are given in Table 1. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Node degrees for interference graphs 300, 301, 
               
               
                 and 302 in respective FIGS. 3A, 3B, and 3C. 
               
            
           
           
               
               
               
               
               
            
               
                 Interference Graph 
                 Node 310 
                 Node 312 
                 Node 314 
                 Node 316 
               
               
                   
               
               
                 300 
                 2 
                 2 
                 1 
                 1 
               
               
                 301 
                 2 
                 3 
                 2 
                 1 
               
               
                 302 
                 3 
                 3 
                 3 
                 3 
               
               
                   
               
            
           
         
       
     
     Next, a “node degree change” may be defined as the change in node degree for a given network node between a previous power level and a current power level. The node degree change variable (Delta_l for power level l with respect to a previous power level l−1) may reflect whether a network has a higher chance of re-using the channels with smaller power level. A smaller value for Delta_l implies smaller chances of re-use with decreasing power level and, therefore, suggests that a larger power level may desirably be used for a given network, when possible. Conversely, a larger value for Delta_l implies a sparser interference graph with decreasing power level and, hence, suggests more chances of spectrum re-use with a lower power level. Accordingly, Delta_l, given in Table 2 for interference graphs  300 ,  301 , and  302 , is utilized to construct channel and network sets. 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Node degree change (Delta_l) for interference graphs 
               
               
                 301 and 302 in respective FIGS. 3A, 3B, and 3C. 
               
            
           
           
               
               
               
               
               
            
               
                 Interference Graph 
                 Node 310 
                 Node 312 
                 Node 314 
                 Node 316 
               
               
                   
               
               
                 301 (Delta_2) 
                 0 
                 1 
                 1 
                 0 
               
               
                 302 (Delta_3) 
                 1 
                 0 
                 1 
                 2 
               
               
                   
               
            
           
         
       
     
     It is further assumed that a total number of channels available is greater than a maximum node degree of an interference graph corresponding to the smallest power level (I — 1). Furthermore, at a given power value (p_l), the algorithm enforces the number of channels in a channel set (S_l) to be greater than a maximum node degree of an interference graph (G_l) comprising the networks in network set (N_l). This update design metric may guarantee an integer channel assignment solution with only one power level across all channels. 
     One embodiment of an algorithm for parallel resource management in white space bands will now be described in detail. Various notations and the corresponding definitions are given in Table 3 below. 
     
       
         
           
               
               
             
               
                   
               
               
                 Notation 
                 Definition 
               
               
                   
               
             
            
               
                 p_l 
                 a power value for power level l 
               
               
                 S_l 
                 a set of channels (from the available channels) that may operate with maximum 
               
               
                   
                 power value p_l 
               
               
                 N_l 
                 a set of networks to which channels from the channel set S_l are assigned 
               
               
                 
                   
                     N 
                   
                 
                 a set of all networks, such that after constructing the network sets N_1 U . . . U 
               
               
                   
                 N_L =    N     
               
               
                 I_l 
                 an interference graph where the nodes denote the networks and the edges reflect 
               
               
                   
                 whether two networks interfere or not, assuming all nodes transmit at a maximum power 
               
               
                   
                 level p_l. 
               
               
                 G_l 
                 An interference graph at power level p_l corresponding to networks set N_l 
               
               
                 Delta_l 
                 a node degree change for a graph at a power level (I_l) with respect to the graph 
               
               
                   
                 at a previous power level (I_{l−1}) 
               
               
                 \delta_l 
                 a maximum node degree in graph G_l 
               
               
                   
               
            
           
         
       
     
     The algorithm described herein may have a polynomial-time complexity of O(K L 2  N 3 ). An inner loop may iterate over values of Delta_l up to a maximum possible node degree change, N−1, and has maximum L iterations. The channel set updates may iterate up to a maximum (L−1)*K (total number of channels). Checking the re-use pairs may have O(N 2 ) complexity. For the channel and network sets obtained, a desired channel assignment algorithm (not described in detail herein) may be executed in parallel to distribute the channels from each channel set to the corresponding network set. For example, the channel assignment algorithm may be based on a greedy graph coloring and/or another algorithm having polynomial-time complexity. Thus, the complexity for the overall joint power control and channel assignment solution described herein may be polynomial. 
     The algorithm described herein to split the channels and networks may receive as input at least identities and location information for N networks. In certain embodiments, the algorithms and methods described herein may be implemented by a white space database manager, such that a white space database may suggest the list of channels with the recommended power levels to each network, corresponding to the output of the methods described herein. Such a service may be expressly permitted by certain FCC regulations and may be supported by standards such as IEEE 802.19.1. Additionally, a central entity splitting the networks and channels may further execute a channel assignment algorithm (not described in detail herein) and may assign orthogonal channels with corresponding power levels to each network, based on the network sets and channel sets generated. 
     In a first step, the algorithm may comprise splitting the available channels into disjoint channels sets S_l where each channel in S_l may transmit at a maximum power level corresponding to power value p_l. As noted above with respect to  FIGS. 3A-3C , for each power level l, an interference graph, G_l, may be constructed under the assumption that an operating frequency of the lowest available spectral band is used, such that G_l represents the most conservative graph in terms of bandwidth for a given power level. 
     In a second step, the algorithm may comprise splitting the available networks into disjoint sets where a network in network set N_l may be assigned channels from set S — 1. It is noted that a network in network set N_l may only be assigned channels from a single channel set S_l to comply with the white space regulations, which would require reducing a larger power level from channels in different channel sets when aggregating such channels. Furthermore, network set N_l may be constructed such that a number of channels in S_l is greater than a value for \delta — 1 for a given graph G_l. From graph coloring theory, this condition ensures an integer channel assignment solution to the algorithm. 
     One objective of the algorithm may be to first utilize the channels with larger power levels in as many networks as possible, and then to increase spectrum re-use. Therefore, networks are included in network set N_l′ (corresponding to a larger power level p_l′) as long as there exist enough channels in channel set S_l′ to assign to these networks. Then, network sets at lower power levels may be updated. Since these lower power network sets may have lower density interference graphs, they may provide more re-use options for given channels. 
     The heuristic approach used in the algorithm is motivated by the following observations:
         using larger power (for substantially the same bandwidth) provides larger signal-to-noise ratio (SNR) and thus may improve the achievable throughput; and   using larger bandwidth (i.e., aggregation of more than one channel with substantially the same power level) may improve the achievable throughput.       

     However, using larger power level with smaller bandwidth (e.g., one white space channel) may achieve a better throughput than using a smaller power level with larger bandwidth (e.g., aggregation of two channels), because the maximum transmit power is limited to the lowest permissible power level regardless of the number of channels that may be aggregated. 
     Accordingly, certain design criteria may be applied to the algorithm. For one, channel sets may be constructed starting with channel sets including any channel having maximum power level p_l. Also, network sets may be construed starting with networks in larger power levels and particularly including networks with smaller Delta_l values, because such networks will have a smaller chance of channel re-use with the lower power level. As such, in order to increase utilization of power resources, these networks will be included in N_l as long as enough channels are available in S_l. Furthermore, channel sets may be updated when not enough channels are available in S — 1 to include in any remaining networks, with Delta — 2 taking any values from 0, 1, . . . , N−1. According to the channel set construction criteria, channel sets may be updated by moving one channel at a time from the channel set corresponding to the largest power value, p_k, where k may take a value L, L−1, . . . , 2, to the channel set having p_{k−1}. 
     Turning now to  FIG. 4 , a block diagram of selected elements of an embodiment of method  400  for parallel white space resource management is shown in flow chart format. As noted above, method  400  may be used for locations where N networks share K white space channels, with some channels having different power levels, up to L power levels. Method  400  may be performed by management system  200  and may represent operations performed by parallel resource management  214  (see  FIGS. 1 and 2 ). It is noted that certain operations depicted in method  400  may be rearranged or omitted, as desired. 
     Method  400  may begin at operation  401 . In some embodiments, N number of networks and their respective locations may be identified during (or prior to) operation  401 . For example, management system  200  may receive the identities and locations of the N number of networks and then output corresponding network sets and channel sets. The channel sets may be initialized (operation  402 ) starting with channels having maximum power level values. The channel sets may be initialized as S_l={set of channels with maximum power level p_l}, where l=1, 2, . . . , L. The network sets corresponding to the L power levels may be initialized (operation  404 ) including maximizing a number of networks in a maximum power network set, and emptying network sets other than the maximum power network set. The maximum power network set corresponds to the maximum power level. The network sets N — 1, . . . , N_{L−1} may initially be empty to fulfill the objective of first utilizing channels with the largest power level in as many networks as possible. Therefore, as many networks/re-use pairs (pairs of networks that are not neighbors and hence may re-use the same assigned channel) as possible may be included in N_L, such that the corresponding graph G_L has a node degree \delta_L=0 (i.e., graph G_L is a disconnected graph). When selecting one from multiple networks/re-use pairs is required, the network with minimum Delta_L along with its re-use pairs, if any, may be included in N_L. Thus, by having at least one channel in S_L, networks in N_L will get a channel assigned. For empty network sets, \delta_l=−1 may be initially defined, which may be used to evaluate the condition to add more networks to a given network set N_l according to the available channels with power level p_l. 
     Next in method  400 , a decision may be made whether every network is included in a network set (operation  406 ). When the result of operation  406  is YES, the network sets and the channel sets may be output (operation  408 ) and method  400  may end (operation  410 ). When the result of operation  406  is NO, the network sets may be updated (operation  412 , see also  FIG. 5 ). Depending on the results of operation  412 , method  400  may return to operation  406  or proceed to update (operation  414 ) the channel sets by moving one channel at a time to a channel set at a next lower power level. In other words, one channel may be moved in operation  414  from S_k to S_{k−1}. The channel sets may be updated by moving one channel at a time from the non-empty channel set corresponding to the largest power level so far, p_k, k=L, L−1, . . . , 2, to the one with p_{k−1}, which may increase the chance of more networks being included in the set corresponding to the lower power levels. Then, a decision may be made whether the channel set for power level=2 is empty (operation  416 ). When the result of operation  416  is NO, method  400  may return to operation  404 . When the result of operation  416  is YES, singular network sets and channel sets may be output (operation  418 ) and method  400  may end (operation  410 ). For network set N_ 2 , any remaining networks in operation  414  with a given value of Delta — 2 not included in N — 2 (because up to n — 2 networks/re-use pairs are already included) may be included in N — 1 corresponding to the channel set with the smallest power level (and hence maximum re-use possibility). However, if the number of channels in N — 1 is not enough (i.e., is less than \delta — 1+1), network splitting is not feasible and the current channel sets may be desirable for updating. When network splitting is not feasible, the S — 1 may represent the channel set of all available channels and N — 1 may represent the network set of all available networks, with all other channel sets and networks sets (for other values of l) remaining empty. 
     Turning now to  FIG. 5 , a block diagram of selected elements of an embodiment of method  500  for parallel white space resource management is shown in flow chart format. Method  500  may represent an embodiment of operation  412  described above with respect to method  400  (see  FIG. 4 ). It is noted that certain operations depicted in method  500  may be rearranged or omitted, as desired. Method  500  may start with updating network sets from larger power levels. In particular, for N_l, networks with smaller Delta_l (starting from networks with Delta_l=0) may be included first, as discussed earlier. The number of networks included in N_l may depend on the number of available channels in S_l and the current maximum node degree of G_l. In order to provide a feasible channel assignment, for any value of Delta_l, up to n_l=|S_l|−\delta_l−1 networks/re-use pairs from the remaining network set (i.e. N\N — 1U . . . U N_L) will be included in network set N_l (and then \delta_l will be updated). For any network for a given value of Delta_l, method  500  may check if there are any other non-adjacent network(s). Then a network may be picked along with its re-use pairs (if applicable). Each re-use pair is counted as 1 group. Furthermore, higher priority may be given for including a re-use pair than a network. If multiple options (more than n_l) are available, the re-use pairs with minimum sum Delta_l may be chosen and finally break the ties, randomly. 
     Method  500  may begin by incrementing a counter i and setting l=k (operation  502 ). Then a decision may be made whether l&gt;1 (operation  504 ) to start a loop. When the result of operation  504  is NO, method  500  may end the loop and proceed to operation  514  (described below). When the result of operation  504  is YES, method  500  may let n_l=|S_l|−\delta_l−1 (operation  506 ). Then a decision may be made whether n_l&gt;0 (operation  508 ). When the result of operation  508  is YES, up to n_l re-use pairs and networks from the remaining network set (i.e. N\N — 1U . . . U N_L) with Delta_l=i in N_l may be selected (operation  510 ). After operation  510  or when the result of operation  508  is NO, l may be decremented (operation  512 ) and method  500  may return to operation  504 . When the result of operation  504  is NO, method  500  may let n — 1=|S — 1|−\delta — 1−1 (operation  514 ). Then, a decision may be made whether n — 1&gt;0 and a number of re-use pairs and networks with (Delta — 2=i)&lt;=n — 1 (operation  516 ). When the result of operation  516  is NO, method  500  may return to operation  414  in method  400  (see  FIG. 4 ). When the result of operation  516  is YES, re-use pairs and networks with (Delta — 2=i) may be included (operation  518 ) in N — 1, after which method  500  may return to operation  406  in method  400  (see  FIG. 4 ). 
     Turning now to  FIGS. 6A and 6B , selected elements on an embodiment of an example of parallel white space resource management are shown. In the example of  FIGS. 6A and 6B , the algorithm described above with respect to  FIGS. 4 and 5  is applied to a topology of 4 networks (N 1 , N 2 , N 3 , and N 4 ) assumed to share  3  white space channels (a, b, and c). In  FIG. 6A , interference graph  600  shows the topology for power level 1 in graph G — 1, which corresponds to channels a and b at a power level 1 value of 40 mW. In  FIG. 6B , interference graph  601  shows the topology for power level 2 in graph G — 2, which corresponds to channel c at a power level 2 value of 100 mW. 
     In one example, when no power control is employed (i.e., all channels transmit with 40 mW power level), in some cases, networks will get 10 MHz bandwidth and in some cases networks will get 5 MHz bandwidth (with the total utilization of 30 MHz). Hence, on average, every network may be allocated about 7.5 MHz bandwidth. Using the algorithm described herein, the following results may be obtained: S — 1={a, b}, S — 2={c}, N — 1={1,4} and N — 2={2,3}. It is noted that this algorithm generates the network sets and the corresponding channel sets, such that the channels from a channel set may be assigned to the corresponding network set. Various additional methods may then be used for channel assignment, as desired. 
     After channel assignment, for example, networks N 2  and N 3  may be assigned channel c at 100 mW power, while networks N 1  and N 4  may be assigned both channels a and b at 40 mW power. In an uncoordinated baseline policy, WiFi networks choose the channel with the least congestion, and LTE networks choose the channels with minimum interference level. It may be observed that, by utilizing more power levels along with coordinated orthogonal channel assignment, throughput performance may be significantly improved compared to the uncoordinated baseline policy and using no power control policies. In particular, it may be observed that, even though networks N 2  and N 3  (assumed to employ IEEE 802.11 access technology) are allocated larger average bandwidth in the uncoordinated baseline policy, the throughput performance of networks N 2  and N 3  is worse than the case with power control using the algorithm described herein, which allocates larger power but smaller bandwidth. For networks N 1  and N 4  (assumed to employ LTE access technology), it may be observed that throughput performance is also better using the methods described herein, since the allocated bandwidth for such cases remains at 10 MHz whereas using the uncoordinated baseline policy, networks N 1  and N 4  would get 5 MHz in some cases and 7.5 MHz on average. 
     The above disclosed subject matter is to be considered illustrative, and not restrictive, and the appended claims are intended to cover all such modifications, enhancements, and other embodiments which fall within the true spirit and scope of the present disclosure. Thus, to the maximum extent allowed by law, the scope of the present disclosure is to be determined by the broadest permissible interpretation of the following claims and their equivalents, and shall not be restricted or limited by the foregoing detailed description.