Patent Publication Number: US-2010110950-A1

Title: Method and apparatus for aligning power savings classes

Description:
TECHNICAL FIELD 
     The present disclosure relates generally to methods and devices for wireless communication systems and, more particularly, to methods and devices for wireless communication systems to provide power savings. 
     BACKGROUND 
     Due to an increasing number of wireless devices and a growing demand for wireless services, wireless communication systems continue to expand. To meet the growing demand, and to increase interoperability and reduce costs, various sets of standards have been introduced for wireless communications. One such set of standards developed for wireless communication is Institute of Electrical and Electronics Engineers, Inc. (IEEE) 802.16. IEEE 802.16 includes the family of standards developed by the IEEE 802.16 committee, establishing standards for broadband wireless access. In part, the IEEE 802.16 family of standards defines interoperability of broadband Wireless Metropolitan Area Networks (WirelessMAN). Generally speaking, WirelessMANs are large networks utilizing wireless infrastructure to form connections between subscriber stations. Wi-Max, a term defined and promoted by The Wi-Max Forum™, is commonly used to refer to WirelessMANs and wireless communication and communication networks that are based on the IEEE 802.16 standard. As used herein, the term “Wi-Max” refers to any communication network, system, apparatus, device, method, etc. that utilizes or is based on the 802.16 family of standards. Included in the 802.16 family of standards is the IEEE 802.16e standard, which relates to mobile Wi-Max. The IEEE 802.16e standard proposes grouping connections according to their Quality of Service types to create Power Saving Classes (PSC). Each type of PSC has a set of message exchange procedures for its definition/activation/deactivation. Moreover, IEEE 802.16e defines a general set of parameters and rules that can be used to design different sleep and listening windows. IEEE 802.16 enumerates three kinds of PSCs:
         Type I Power Saving Class (Type 1 PSC): Groups together BE and NRT-VR connections. A fixed length listening window alternates with a sleep window, where each sleep window is twice the size of a previous sleep window, to some maximum sleep window size.   Type II Power Saving Class (Type 2 PSC): Groups together UGS, ERT-VR, and RT-VR connections. A fixed length listening window alternates with a fixed length sleep window.       

     Type III Power Saving Class (Type 3 PSC): Groups together multicast connections and management connections. A single sleep window whose duration is based on an expected time period before activity. The duration and separation of the expected time period of activity and the sleep window, i.e., the expected time period before activity is set based on an expected arrival of a next portion of data or next expected ranging request. 
     In addition, IEEE 802.16e supports a device mode. A device mode provides energy savings on a mobile station when the traffic load is low. A device mode consists of alternating unavailability intervals and availability intervals. Generally, during the unavailability interval the device cuts off all contact with its serving base station and conserves its energy. During the availability interval, the device actively waits for traffic and/or sends packets out. The unavailability interval is defined in IEEE 802.16e as a time interval that does not overlap with any listening window of any active PSC. The availability interval is defined in IEEE 802.16e as a time interval that does not overlap with any unavailability interval. 
     IEEE 802.16e defines the relationship between unavailability intervals and availability intervals. 
     The disclosed embodiments are directed to overcoming one or more of the problems set forth above. 
     SUMMARY 
     In one exemplary embodiment, the present disclosure is directed to a method for power savings in a wireless communications network, comprising: selecting all Type 1 power savings classes (PSCs), if present on a device; selecting all Type 2 PSCs, if present on the device; selecting all Type 3 PSCs, if present on the device; aligning the selected Type 1 PSCs of the device, if more than one Type 1 PSC is selected; aligning the selected Type 2 PSCs of the device, if more than one Type 2 PSC is selected; aligning the two or more aligned Type 1 PSCs or, if only one Type 1 PSC is selected, the selected Type 1 PSC, and the two or more aligned Type 2 PSCs or, if only one Type 2 PSC is selected, the selected Type 2 PSC, if there is at least one selected Type 1 PSC and at least one selected Type 2 PSC; and aligning the selected Type 3 PSCs with the aligned Type 1 and Type 2 PSCs, if there is at least one selected Type 3 PSC and at least one Type 1 or Type 2 PSC. 
     In another exemplary embodiment, the present disclosure is directed to a wireless communication mobile station for wireless communication, comprising: at least one memory to store data and instructions; and at least one processor configured to access the memory and execute instructions. The processor is configured to, when executing the instructions: select all Type 1 power savings classes, if present on a device; select all Type 2 power savings classes, if present on the device; select all Type 3 power savings classes, if present on the device; align the selected Type 1 power savings classes of the device, if more than one Type 1 power savings class is selected; align the selected Type 2 power savings classes of the device, if more than one Type 2 power savings class is selected; align the two or more aligned Type 1 power savings classes or, if only one Type 1 power savings class is selected, the selected Type 1 power savings class, and the two or more aligned Type 2 power savings classes or, if only one Type 2 power savings class is selected, the selected Type 2 power savings class, if there is at least one selected Type 1 power savings class and at least one selected Type 2 power savings class; and align the selected Type 3 power savings classes with the aligned Type 1 and Type 2 power savings classes, if there is at least one selected Type 3 power savings class and at least one Type 1 or Type 2 power savings class. 
     In a further exemplary embodiment, the present disclosure is directed to a computer-readable medium including instructions for performing a method, when executed by a processor, for power savings in a wireless communications network, the method comprising: selecting all Type 1 power savings classes, if present on a device, wherein each of the one or more Type 1 power savings classes has a series of equal fixed duration listening windows alternating with a series of sleep windows, and wherein each sleep window has twice a duration of a previous sleep window, up to a maximum sleep window duration, and an initial sleep window duration is greater than or equal to the listening window fixed duration; selecting all Type 2 power savings classes, if present on the device, wherein each of the one or more Type 2 power savings classes has a series of equal fixed duration listening windows alternating with a series of equal fixed duration sleep windows and the sleep window duration is greater than the listening window duration; selecting all Type 3 power savings classes, if present on the device, wherein each of the one or more Type 3 power savings classes has a sleep window wherein durations and separations of an expected time period of activity and the sleep window is set based on an expected arrival of a next portion of data or next expected ranging request; aligning the selected Type 1 power savings classes of the device, if more than one Type 1 power savings class is selected; aligning the selected Type 2 power savings classes of the device, if more than one Type 2 power savings class is selected; aligning the two or more aligned Type 1 power savings classes or, if only one Type 1 power savings class is selected, the selected Type 1 power savings class, and the two or more aligned Type 2 power savings classes or, if only one Type 2 power savings class is selected, the selected Type 2 power savings class, if there is at least one selected Type 1 power savings class and at least one selected Type 2 power savings class; aligning the selected Type 3 power savings classes with the aligned Type 1 and Type 2 power savings classes, if there is at least one selected Type 3 power savings class and at least one Type 1 or Type 2 power savings class; and communicating the alignment of any Type 1, Type 2, or Type 3 power savings classes to a base station. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram of an exemplary Wi-Max network; 
         FIG. 2   a  is a block diagram of an exemplary Base Station, consistent with certain disclosed embodiments; 
         FIG. 2   b  is a block diagram of an exemplary Stationary Station, consistent with certain disclosed embodiments; 
         FIG. 2   c  is a block diagram of an exemplary Mobile Station, consistent with certain disclosed embodiments; 
         FIG. 3  is a flow chart illustrating an exemplary power saving mode request consistent with certain disclosed embodiments; 
         FIG. 4   a  is an exemplary diagram including a horizontal time axis, illustrating availability and unavailability intervals of a mobile device based on sleep and listening windows of multiple unaligned PSCs, consistent with certain disclosed embodiments; 
         FIG. 4   b  is an exemplary diagram including a horizontal time axis, illustrating availability and unavailability intervals of a mobile device based on sleep and listening windows of multiple aligned PSCs, consistent with certain disclosed embodiments; 
         FIG. 5  is an exemplary diagram including a horizontal time axis, illustrating availability and unavailability intervals of a mobile device based on sleep and listening windows of two unaligned Type 2 PSCs, consistent with certain disclosed embodiments; 
         FIG. 6  is an exemplary diagram including a horizontal time axis, illustrating availability and unavailability intervals of a mobile device based on sleep and listening windows of two Type 2 PSCs and one Type 1 PSC that are aligned by sleep window start times, consistent with certain disclosed embodiments; 
         FIG. 7  is an exemplary diagram including a horizontal time axis, illustrating availability and unavailability intervals of a mobile device based on sleep and listening windows of two Type 2 PSCs and one Type 1 PSC that are aligned to place longer unavailability intervals at the start of a cycle, consistent with certain disclosed embodiments; 
         FIG. 8  is a flow chart illustrating an exemplary method to align three or more Type 2 PSCs, consistent with certain disclosed embodiments; 
         FIG. 9   a  is an exemplary diagram including a horizontal time axis, illustrating availability and unavailability intervals of a mobile device based on sleep and listening windows of five Type 1 PSCs that are aligned by initial sleep window start time, consistent with certain disclosed embodiments; 
         FIG. 9   b  is an exemplary diagram including a horizontal time axis, illustrating availability and unavailability intervals of a mobile device based on sleep and listening windows of five Type 1 PSCs that are aligned, consistent with certain disclosed embodiments; 
         FIG. 10  is a flow chart illustrating an exemplary method to align three or more Type 1 PSCs, consistent with certain disclosed embodiments; 
         FIG. 11  is an exemplary diagram including a horizontal time axis, illustrating availability and unavailability intervals of a mobile device based on sleep and listening windows of multiple PSCs with different PSC Types that are aligned, consistent with certain disclosed embodiments; 
         FIG. 12  is a flow chart illustrating an exemplary method to align multiple PSCs with different PSC Types, consistent with certain disclosed embodiments; 
         FIG. 13  is an exemplary diagram including a horizontal time axis, illustrating available and unavailable intervals of a mobile device based on sleep and listening windows of multiple PSCs where the initial sleep window of a Type 1 PSC is greater than the sleep window of a Type 2 PSC and the listening window of the Type 1 PSC is greater than the listening window of the Type 2 PSC, consistent with certain disclosed embodiments; 
         FIG. 14  is an exemplary diagram including a horizontal time axis, illustrating available and unavailable intervals of a mobile device based on sleep and listening windows of multiple PSCs where the sleep window of a Type 2 PSC is greater than the initial sleep window of a Type 1 PSC and the listening window of the Type 2 PSC is greater than the listening window of the Type 1 PSC, consistent with certain disclosed embodiments; 
         FIG. 15  is an exemplary diagram including a horizontal time axis, illustrating available and unavailable intervals of a mobile device based on sleep and listening windows of multiple PSCs where the sleep window of a Type 2 PSC is greater than or equal to the initial sleep window of a Type 1 PSC and the listening window of the Type 1 PSC is greater than the listening window of the Type 2 PSC, consistent with certain disclosed embodiments; 
         FIG. 16  is an exemplary diagram including a horizontal time axis, illustrating available and unavailable intervals of a mobile device based on sleep and listening windows of multiple PSCs where the sleep window of a Type 2 PSC is greater than or equal to the initial sleep window of a Type 1 PSC and the listening window of the Type 1 PSC is equal to the listening window of the Type 2 PSC, consistent with certain disclosed embodiments; 
         FIG. 17  is an exemplary diagram including a horizontal time axis, illustrating available and unavailable intervals of a mobile device based on sleep and listening windows of multiple PSCs where the initial sleep window of a Type 1 PSC is greater than or equal to the sleep window of a Type 2 PSC and the listening window of the Type 2 PSC is greater than the listening window of the Type 1 PSC, consistent with certain disclosed embodiments; and 
         FIG. 18  is an exemplary diagram including a horizontal time axis, illustrating available and unavailable intervals of a mobile device based on sleep and listening windows of multiple PSCs where the initial sleep window of a Type 1 PSC is greater than the sleep window of a Type 2 PSC and the listening window of the Type 2 PSC is equal to the listening window of the Type 1 PSC. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  is a block diagram of an exemplary Wi-Max network  100  based on the IEEE 802.16 family of standards, consistent with certain disclosed embodiments. As shown in  FIG. 1 , Wi-Max network  100  may include one or more transmitters, e.g., base stations (BS)  110 , including BSs  110   a ,  110   b , and  110   c , one or more receivers, e.g., stationary stations (SS)  120 , including SSs  120   a  and  120   b , and mobile stations (MS)  130 , including MSs  130   a ,  130   b , and  130   c . While the discussion of  FIG. 1  will be made with reference to the IEEE 802.16 family of standards, it is to be understood that the systems and methods disclosed herein may be used in any type of network having a plurality of nodes and remote communication stations. 
     The one or more BSs  110  may include any type of communication device configured to transmit and/or receive communications based on the IEEE 802.16 family of standards, many of which are known in the art. In one exemplary embodiment, the one or more BSs  110  are connected by transmission paths  140  (TP) to a network  150 . In addition, BSs  110  may be configured to communicate with one or more SSs  120 , MSs  130 , and/or other BSs  110  using communication protocols on communication path  160   s  (CP) also defined by the 802.16 family of standards. In one exemplary embodiment, BSs  110  serves as an intermediary between one or more SSs  120 , MSs  130 , or BSs  110  and network  150 . Communication with network  150  may be made via wired connections, wireless connections, or any combination thereof. Network  150  can include, for example, any combination of one or more WANs, LANs, intranets, extranets, Internet, etc. 
     SSs  120  and MSs  130  may include any type of wireless client device configured to communicate with BS  110  and/or other SSs  120  and MSs  130  using the communication protocols on CP  160  defined by the 802.16 family of standards. Each SS  120  and MS  130  may include, for example, servers, clients, mainframes, desktop computers, laptop computers, network computers, workstations, personal digital assistants (PDA), tablet PCs, scanners, telephony devices, pagers, cameras, musical devices, etc. In one exemplary embodiment, SS  120  is a Wi-Fi device enabled to communicate with BS  110  using the communication protocols on CP  160  defined by the 802.16 family of standards. Each BS  110  has a broadcast range within which that BS  110  can communicate with SS  120 , MS  130 , and one or more other BSs  110 . Broadcast ranges of each BS  110  may vary due to power levels, location, interference (physical and/or electromagnetic), etc. Similarly, each SS  120  and MS  130  has a broadcast range within which that SS  120  and MS  130  may communicate with one or more other SSs  120 , MSs  130  and/or BSs  110 . Broadcast ranges of each SS  120  and MS  130  may vary due to power levels, location, interference (physical and/or electromagnetic), etc. In addition to the ability of each BS  110  to connect and communicate with SS  120  and MS  130 , each BS  110  may also connect and communicate with one or more other BSs  110  using a line-of-sight, wireless link using the protocols and standards defined by the IEEE 802.16 family of standards. 
     TP  140  is a transmission path that may include one or more nodes in network  100 . TP  140  may be wired, wireless, or any combination of wired and/or wireless communication means and/or methods. 
     Still referring to  FIG. 1 , BS  110  may be configured to create and store one or more data structures associated with one or more SSs  120 , MSs  130 , TPs  140 , and/or one or more CPs  160 , as well as to create and store one or more relationships between the data structures. For example, BS  110  may store one or more subscriber or mobile station identifiers, one or more transmission path identifiers, one or more communication path data structures, one or more transmission path data structures, etc. 
     In addition, MS  130  may be configured to create and store one or more data structures associated with one or more BSs  110 , SSs  120 , MSs  130 , TPs  140 , and/or one or more CPs  160 , as well as to create and store one or more relationships between the data structures. For example, MS  130  may store data on one or more of: all known connections, the period of threshold communication activity, power savings classes, one or more subscriber or mobile station identifiers, one or more transmission path identifiers, one or more communication path data structures, one or more transmission path data structures, etc. 
       FIG. 2   a  is a block diagram of an exemplary structure of BS  110 . As shown in  FIG. 2   a , BS  110  may include one or more of the following components: at least one central processing unit (CPU)  211  configured to execute computer program instructions to perform various processes and methods, random access memory (RAM)  212  and read only memory (ROM)  213  configured to access and store information and computer program instructions, memory  214  to store data and information, one or more databases  215  to store tables, lists, or other data structures, one or more input/output (I/O) devices  216 , one or more interfaces  217 , one or more antennas  218 , etc. Each of these components is well-known in the art and will not be discussed further. 
       FIG. 2   b  is a block diagram of an exemplary structure of SS  120 . As shown in  FIG. 2   b , SS  120  may include one or more of the following components: at least one CPU  221  configured to execute computer program instructions to perform various processes and methods, RAM  222  and ROM  223  configured to access and store information and computer program instructions, memory  224  to store data and information, one or more databases  225  to store tables, lists, or other data structures, one or more I/O devices  226 , one or more interfaces  227 , one or more antennas  228 , etc. Each of these components is well-known in the art and will not be discussed further. 
     SS  120  may include any type of wireless client device configured to communicate with BSs  110 , other SSs  120 , and/or MSs  130  using one or more wireless communication standards including, for example, the IEEE 802.16 family of standards. SSs  120  may include, for example, servers, clients, mainframes, desktop computers, laptop computers, network computers, workstations, tablet PCs, scanners, telephony devices, pagers, cameras, musical devices, etc. The location of SS  120  is stationary and SS  120  is expected to remain in contact with the same group of BSs  110  and SSs  120 . 
       FIG. 2   c  is a block diagram of an exemplary structure of MS  130 . As shown in  FIG. 2   c , MS  130  may include one or more of the following components: at least one CPU  231  configured to execute computer program instructions to perform various processes and methods, RAM  232  and ROM  233  configured to access and store information and computer program instructions, memory  234  to store data and information, one or more databases  235  to store tables, lists, or other data structures, one or more I/O devices  236 , one or more interfaces  237 , one or more antennas  238 , etc. Each of these components is well-known in the art and will not be discussed further. 
     MS  130  may include any type of wireless client device configured to communicate with BSs  110 , SSs  120 , and/or other MSs  130  using one or more wireless communication standards including, for example, the IEEE 802.16 family of standards. MSs  130  may include, for example, servers, clients, mainframes, desktop computers, laptop computers, network computers, workstations, personal digital assistants (PDA), tablet PCs, scanners, telephony devices, pagers, cameras, musical devices, etc. In one exemplary embodiment, MS  130  is a mobile computing device. In other embodiments, MS  130  is a “non-mobile” computing device located in a mobile environment (e.g., airplanes, watercraft, buses, multi-passenger vehicles, automobiles, etc.). 
       FIG. 3  is a flow chart  300  of an exemplary power saving mode request consistent with IEEE 802.16e. In step  302 , MS  130  monitors a threshold communications inactivity period and determines if a prerequisite period of threshold communication inactivity has been met. If the prerequisite period of threshold communication inactivity has not been met, MS  130  waits for a duration, then checks step  302  again. In step  304 , after the prerequisite period of threshold communication inactivity has exceeded its threshold, MS  130  sends a mobile station sleep request MOB_SLP-REQ to BS  110  to negotiate a sleep window. The MOB_SLP-REQ contains information from MS  130  necessary to implement power savings. In step  306 , BS  110  responds with a mobile station sleep response MOB_SLP-RSP including its response to the request to negotiate a sleep window from MS  130 . In step  308 , MS  130  determines if the response to its sleep window request was proper and positive. If the response was not proper and positive, MS  130  repeats step  304 . If the response was proper and positive, in step  310  MS  130  enters a power savings mode at an appropriate time in accordance with the received sleep response. 
     In one exemplary embodiment, a power savings mode may include alternating sleep windows and listening windows. During the sleep window, MS  130  cuts off all contact with its serving BS  110  and conserves its power, or uses its power for other tasks. During the listening window, MS  130  actively waits for traffic and/or sends out packets. 
     The power saving mode has several PSCs. In one exemplary embodiment, the above noted three PSCs of IEEE 802.16e are configured as follows. In a Type 1 PSC, sleep windows increase in size at each sleep window by doubling the previous sleep window until a determined maximum sleep window size is reached at which the sleep window size remains unchanged. The listening window may be maintained at a fixed duration. A Type 2 PSC has sleep and listening windows of fixed duration. Type 2 PSCs are composed primarily of UGS, ERT-VR, and RT-VR connections. A Type 3 PSC has its sleep window duration set based on the expected arrival of the next portion of data or next expected ranging request. Periodically a ranging request may be used to determine the distance between a MS  130  and any BS  110  within range of MS  130 . Ranging and range requests are well known in the art and will not be further discussed. 
     PSC listening windows, sleep windows, availability intervals, and unavailability intervals, each have a duration, which is a measurement in time. In one exemplary embodiment, the measurement in time is a frame. A frame in one exemplary embodiment may have a duration between 2 milliseconds and 20 milliseconds. In other exemplary embodiments, a frame may be a shorter or a longer duration. As used below, length, when referring to a PSC listening window, sleep window, availability interval, and unavailability interval, is referring to the duration in time, not to a physical measurement of distance. 
     A plurality of PSCs are formed from selecting connections with common performance characteristics. Quality of Service (QoS) types can be used to sort connections into PSCs with similar performance characteristics. After selecting connections with common performance characteristics to create a plurality of PSCs respectively composed of connections with similar characteristics, a power savings window size is determined for each PSC. The determination of power savings window size includes determining the sizes of listening windows and sleep windows. Desirably, the power savings window sizes are determined to decrease power consumption and maintain QoS performance levels. 
       FIG. 4   a  is an exemplary diagram including a horizontal time axis, illustrating availability and unavailability intervals of a mobile device, e.g., MS  130 , based on sleep and listening windows of multiple PSCs. More particularly,  FIG. 4   a  shows an exemplary embodiment of alignment in which all of the PSCs with the same start time are aligned. PSC-T 2 - 1  (Power Savings Class-Type  2 - 1 ) may have alternating sleep and listening windows. Similarly, PSC-T 2 - 2  and PSC-T 2 - 3  may also have alternating sleep and listening windows. PSC-T 2 - 1 , PSC-T 2 - 2 , and PSC-T 2 - 3  are all Type 2 PSCs, and PSC-T 1 - 4  (Power Savings Class-Type  1 - 4 ) is a Type 1 PSC, and PSC-T 1 - 4  may also have alternating sleep and listening windows. 
     As shown in  FIG. 4   a , MS  130  may have a device mode, as long as the PSCs are active, corresponding to the availability interval and unavailability interval. The device mode is set to unavailable when all of the PSCs&#39; windows are set to sleep. When one or more of the PSCs are in a listening window, the device mode will be set to available. 
       FIG. 4   b  is an exemplary diagram including a horizontal time axis, illustrating availability and unavailability intervals of a mobile device, e.g., MS  130 , based on sleep and listening windows of multiple PSCs. More particularly,  FIG. 4   b  shows an exemplary embodiment of alignment. This example may be created by selecting the start time for each PSC to generate overlap of the sleep windows of the PSC and reduce long availability intervals on the device. The PSCs are the same in  FIGS. 4   a  and  4   b , but in  FIG. 4   b  the unavailability intervals are longer and more evenly spaced. 
     Alignment of multiple PSCs can be accomplished in various ways. The following disclosure provides alignment for multiple Type 1 PSCs or multiple Type 2 PSCs, or a combination of multiple Type 1 PSCs and multiple Type 2 PSCs. Generally, the disclosed embodiments may first sort the PSCs based on type, i.e., sort into different groups of PSC types. Each group of PSC type is then sorted by order, i.e., by increasing or decreasing duration, followed by pair-by-pair alignment of the PSCs of a type. The order of the PSCs in a type and the pair-by-pair alignment is used to align all PSCs within a type. Last, the different aligned types of PSCs are aligned, creating an alignment for all the PSCs. If there are not enough PSCs for a particular step, that step will not be performed for that type of PSC. 
       FIG. 5  is an exemplary diagram including a horizontal time axis, illustrating availability and unavailability intervals of a mobile device, e.g., MS  130 , based on sleep and listening windows of two Type 2 PSCs, PSC-T 2 - 1  and PSC-T 2 - 2 . More particularly,  FIG. 5  shows an alignment as a repetitive cycle for PSC-T 2 - 1  and PSC-T 2 - 2 . As discussed above, a Type 2 PSC has fixed length listening windows alternating with fixed length sleep windows. The listening window of a Type 2 PSC is shorter than the sleep window of the same Type 2 PSC. As shown in  FIG. 5 , for PSC-T 2 - 1 , the sleep window length is X and the listening window length is v1. v1 can be thought of as a vector, and Tv1 as a translation of v in the time domain, where Tv1(X)≡X+v1, the sleep and listening window of a Type 2 PSC. Further, a second or further Type 2 PSC, PSC-T 2 - 2  can be represented by Tv2(Y)≡Y+v2, etc., where for PSC-T 2 - 2  the sleep window length is Y and the listening window length is v2. It will be assumed that in all Type 2 PSCs the listening windows (v1, v2, etc.) are smaller then the smallest sleep window, such as Y. In other words, not only is v1&lt;X, v2&lt;Y, but, v1, v2, etc. &lt;smallest of (X, Y, etc.). 
     The difference in length of two Type 2 PSC, such as PSC-T 2 - 1  and PSC-T 2 - 2 , can be expressed as ρ, where ρ=Tv1(X)−Tv2(Y). There is some number r, where r*ρ=W=Tv2(Y) and it then follows that there must be some n and some m such that m*Tv1(X)=n*Tv2(Y). The greatest common divisor (Gcd) of Tv1(X) and Tv2(Y) can generate m and n such that m*Tv1(X)=n*Tv2(Y). If Gcd(Tv1(X), Tv2(Y))=z, where z is a positive integer, then Ntx=Tv2(Y)/z, Nty=Tv1(X)/z, and Ntx*Tv1(X)=Nty*Tv2(Y). Ntx and Nty are the number of translations of X and Y to have the distance Ntx*Tv1(X)=Nty*Tv2(Y). 
     If Tv1(X) is a multiple of Tv2(Y), then z=Tv2(Y). In other words, the Gcd(Tv1(X), Tv2(Y))=Tv2(Y). An example might be Gcd(9, 3)=3. Further, if z=1, Ntx=Tv2(Y) and Nty=Tv1(x). In other words, Tv1(X)*Tv2(Y)=Tv1(X)*Tv2(Y). Thus, for example, if Gcd(9, 7)=1, Ntx=Tv2(Y)/z=7/1, Nty=Tv1(X)/z=9/1, and Ntx*Tv1(X)=Nty*Tv2(Y)==7*9=9*7=63. 
       Cycle= Ntx*Tv 1( X )= Nty*Tv 2( Y ),  Eq. 1         wherein:
           Ntx is the number of translations of X to equal Nty*Tv2(Y)   Tv1(X) is the duration of a Type 2 PSC X   Nty is the number of translations of Y to equal Ntx*Tv1(X)   Tv2(Y) is the duration of a Type 2 PSC Y   
               
     The cycle defined by equation (1) is the number of translations needed before two different metric spaces (PSCs) repeat their relationship with respect to each other. In other words, a cycle is the duration before two PSCs repeat the same spatial relationship with respect to each other. Thus, a set of instructions that produces a result in a cycle for two Type 2 PSCs will produce the same result in every other cycle of the same two Type 2 PSCs. A round is every translation of X which equals Tv1(X). In other words, a cycle is composed of Ntx rounds of Tv1(X) and Nty rounds of Tv2(Y). 
     For Type 2 PSCs, a set of rules and equations provides a basis for analyzing the possible alignments of a pair of Type 2 PSCs: 
         Tv 1( X )&gt; Tv 2( Y ),  Eq. 2 
       If  U   o   ≧Tv 2( Y ), then set  U   o   =U   o   −Tv 2( Y )  Eq. 3 
       If  U   o   +Y&gt;X,  then set  A=X−U   o  and  v 2 =v 2+( U   o   +Y )− X   Eq. 4 
       Alignment of ( Tv 1( X ),  Tv 2( Y ))=( U   1   +U   2 )+( U   3   +U   4 )+ . . . +( U   n-1   +U   n )  Eq. 5 
         U   1 =( Y+U   o )+ v 2 and  U   2   =U   1 −( X+v 1)  Eq. 6 
         U   3 =( Y+U   2 )+ v 2 and  U   4   =U   3 −( X+v 1)  Eq. 7 
       ( U   1   +U   2 ) 1 +( U   3   +U   4 ) 2 + . . . +( U   n-1   +U   n ) Ntx  rounds with n terms, for  n= 2 *Ntx   Eq. 8 
       If ( X−U   1 )&gt; Y , then set B=Y and  v 1= v 1+(( X−U   1 )− Y )  Eq. 9 
       If ( Y+U   o )&gt;= Y , then set A=Y  Eq. 10 
       For (A,B),  A= ( Y+U   n-2 ),  B= ( X−U   n-1 ), A&gt;0, B&gt;0 if A&lt;0, A=0 and if B&lt;0, B=0 with n=2*Ntx  Eq. 11         wherein:       
     
       
         
           
               
             
               
                 TABLE 1 
               
               
                   
               
               
                 Definitions of Variables for Eq. 2 to Eq. 12 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 Tv1(X) 
                 Duration of a Type 2 PSC X 
               
               
                 Tv2(Y) 
                 Duration of a Type 2 PSC Y 
               
               
                 U O   
                 Difference between the start time of Tv1(X) and Tv2(Y) 
               
               
                 X 
                 Sleep window of Tv1(X) 
               
               
                 Y 
                 Sleep window of Tv2(Y) 
               
               
                 v1 
                 Listening window of Tv1(X) 
               
               
                 v2 
                 Listening window of Tv2(Y) 
               
               
                 Ntx 
                 Number of translations of X to equal Nty * Tv2(Y) 
               
               
                 Nty 
                 Number of translations of Y to equal Ntx * Tv1(X) 
               
               
                 U 1   
                 Difference between the start time of Tv1(X) and 2 * Tv2(Y) 
               
               
                 U 2   
                 Difference between the start time of 2 * Tv1(X) and 2 * Tv2(Y) 
               
               
                 U 3   
                 Difference between the start time of 2 * Tv1(X) and 3 * Tv2(Y) 
               
               
                 U 4   
                 Difference between the start time of 3 * Tv1(X) and 3 * Tv2(Y) 
               
               
                 U n−1   
                 Difference between the start time of (Ntx) * Tv1(X) and 
               
               
                   
                 (Ntx + 1) * Tv2(Y) 
               
               
                 U n   
                 Difference between the start time of (Ntx + 1) * Tv1(X) and 
               
               
                   
                 (Ntx + 1) * Tv2(Y) 
               
               
                 A 
                 First possible unavailability interval for a round 
               
               
                 B 
                 Second possible unavailability interval for a round 
               
               
                   
               
            
           
         
       
     
     Uo is the difference between the start time of Tv1(X) and Tv2(Y). Uo=0 when Tv1(X) and Tv2(Y) have the same start time. 
     Eq. 2 is the condition that the duration of Tv1(X) must be greater than the duration of Tv2(Y). Thus, one of the Type 2 PSCs must be longer then the other, and for consistency herein, the Type 2 PSC with the longer duration will be called Tv1 (X). 
     In Eq. 3, when Uo is greater than or equal to the duration of the shorter Type 2 PSC, Tv2(Y), the duration of Tv2(Y) is subtracted from Uo. For Type 2 PSCs, it is desirable that the shorter Type 2 PSC, e.g., Tv2(Y), starts within its own length of the start time of the longer Type 2 PSC, i.e., Tv1(X). After the first cycle, the next cycle will be a mirror image of the first cycle, except that Tv2(Y) will have its first start of the cycle within its own length of the start time of Tv1(X). 
     In Eq. 4, when the sum of the initial delay Uo and Y, the sleep window of Tv2(Y), is greater than X, the duration of the sleep window of Tv1(X), the listening window of Tv2(Y) is increased by the difference between the sum of the initial delay Uo and the sleep window of Tv2(Y) and the duration of the sleep window of Tv1(X). The listening window of Tv1(X) may overlap with a sleep window of Tv2(Y), and the overlap is added to v2. In this case, the unavailability interval A corresponds to the length of the sleep window of Tv1(X) minus the length of Uo. 
     Eq. 5, 6, and 7 show how to align Tv1(X) and Tv2(Y). First, Uo is selected. Since for two Type 2 PSCs, the sleep windows X and Y are known, as are the listening windows v1 and v2, using Eq. 6 and Eq. 7, all Un for a cycle are calculated. For each U calculated, the conditions of Eq. 3, Eq. 4, Eq. 9, and Eq. 10 are considered, and applied if appropriate. Eq. 5 is presented as a pair of U&#39;s for each round. Each pair of Us may be further broken into the unavailability intervals Y+Un−2 and X−Un−1 and the availability intervals v2 or v1. The unavailability intervals Y+Un−2 and X−Un−1 correspond to A and B in Eq. 11 with n=2*Ntx. Because of the positive sign of Uo in the formulas, Un−1=Y+Un−2+v2 and Un=Un−1−(X+v1) are used only to calculate the U&#39;s of the next round, as in Eq. 6, Eq. 7, and Eq. 8, and not to calculate A and B. 
     In Eq. 8, the relationship between U and the round is shown. U1 and U2 are associated with round 1 (Ntx=1), U3 and U4 are associated with round 2 (Ntx=2), and so on, till Un−1 and Un are associated with round n/2 (Ntx=n/2). In other words, each round has a pair of possible unavailability intervals. 
     In Eq. 9, when the sleep window of Tv1(X) minus U1, which represents the duration of the second unavailability interval for a round, is greater than the duration of the sleep window of Tv2(Y), then also set B=Y for that round. B is the second possible unavailability interval of the round. In this case, the part of the unavailability interval B that overlaps part of the listening window of Tv2(Y) is subtracted from that unavailability interval and added to the availability interval v1. 
     In Eq. 10, when the sleep window of Tv2(Y) plus U0 is greater than or equal to the duration of the sleep window of Tv2(Y), A will be set to Y for that round, which is usually the case unless Uo+Y is also greater than X duration. A is the first possible unavailability interval of the round. If Uo+Y is greater than X, Eq. 4 is applied, otherwise if Uo+Y is greater than or equal to Y, Eq. 10 is applied by setting the first unavailability interval to Y. 
     In Eq. 11, the possible unavailability intervals of each round, A and B, can be calculated. Each round has a pair of possible unavailability intervals. The two intervals, A and B, represent the unavailability interval gain for each round when aligning the sleep windows and listening windows of the two Type 2 PSCs. The gain is measured against the unavailability when the two Type 2 PSCs are started at the same time, in other words, when Uo equals zero. A represents the unavailability from (Y+Uo), (Y+U2) . . . (Y+Un−2). B represents the unavailability from (X−U1), (X−U3) . . . (X−Un−1) with n=2*Ntx (rounds). A and B may be represented as a pair, e.g., (A, B). 
     In Eq. 11, if either A or B is a negative number, then that A or B will be set to zero, and the next availability v1 or v2 will be reduced by the negative value that was found for A or B before A or B was set to zero. In other words, every time there is a negative unavailability interval followed by an availability interval, the availability interval will be decreased by the negative unavailability interval. 
     For n greater than 1, each Un depends in part on the value of Un−1, back to Uo. Because A and B depend on the value of Un−2 and Un−1, respectively, a change in Uo may produce different A and B for n greater or equal to 2. In every round, the total unavailability interval is equal to A+B and the total availability interval is equal to v1+v2. In one exemplary embodiment, v1 and v2 may be adjusted per Eq. 4 and Eq. 9. 
     Therefore, selecting various values of Uo and applying the above relationships leads to the result that the availability interval can be decreased only in the first cycle. The second and subsequent cycles will have the same duration of total availability interval as when Uo=0. To take advantage of the translations being isomorphic to one another, the alignment for two Type 2 PSCs may be defined to be the same as when the longer unavailability intervals are at the start of a cycle. The alignment will lead to a better distribution of the availability intervals. Except for the first cycle, the alignment will not reduce the total length of availability intervals. 
       FIG. 6  is an exemplary diagram including a horizontal time axis, illustrating availability and unavailability intervals of a mobile device, e.g., MS  130 , based on sleep and listening windows of two Type 2 PSCs, PSC-T 2 - 1  and PSC-T 2 - 2 , and one Type 1 PSC, PSC-T 1 - 1 , that are aligned by sleep window start times.  FIG. 7  is an exemplary diagram including a horizontal time axis, illustrating availability and unavailability intervals of a mobile device, e.g., MS  130 , based on sleep and listening windows of two Type 2 PSCs, PSC-T 2 - 1  and PSC-T 2 - 2 , and one Type 1 PSC, PSC-T 1 - 1 , that are aligned to place the longer unavailability intervals at the start of the cycle. Both  FIG. 6  and  FIG. 7  disclose the same two Type 2 PSCs, PSC-T 2 - 1  and PSC-T 2 - 2 , and the same Type 1 PSC, PSC-T 1 - 1 , however, in  FIG. 7 , the PSCs are aligned because the longer unavailability intervals are at the start of the cycle. Longer unavailability intervals at the start of a cycle may produce a benefit when a Type 2 PSC drops out unexpectedly. Longer unavailability intervals at the start of a cycle may also provide more consistent unavailability intervals. Alignment further includes avoiding long availability intervals both at the start of and during a cycle to improve unavailability intervals when three or more PSCs are aligned. When the method is adapted to include aligning three or more Type 2 PSCs, long availability intervals will be added too, increasing the length of the availability intervals. To optimize the unavailability of the device, a method is needed suitable for PSCs with different listening and sleep window sizes. Additionally, the method should be designed to align all the rounds of a PSC, even for randomly selected base sleep window sizes. The method should provide alignment for multiple Type 1 PSCs or multiple Type 2 PSCs, or the combination of multiple Type 1 PSCs and multiple Type 2 PSCs. The method should offer a solution for realistic traffic patterns of PSCs of a wireless network, such as WiMax. 
     In one exemplary embodiment, one set of alignment rules for two Type 2 PSCs may include the following: 
       If  Tv 1( X )= Tv 2( Y ) or Gcd(Tv1(X),  Tv 2( Y ))= Tv 2( Y ), then U o =0  Eq. 12 
       If Gcd(Tv1(X),  Tv 2( Y ))=1 and X&gt;Y, and if v2&gt;v1, 
       then  U   o   =X−Y,  else  U   o   =Tv 1( X )− Tv 2( Y )  Eq. 13 
       If Gcd(Tv1(X),  Tv 2( Y ))=1 but X≦Y (meaning v2&lt;v1 to verify PSC1&gt;PSC2 and Gcd=1 conditions), then  U   o   =Tv 1( X )− Tv 2( Y )  Eq. 14 
       If Gcd(Tv1(X),  Tv 2( Y ))≠1 and smaller than Tv2(Y), and 
       If [X&gt;Y or (Y&gt;X and v1&gt;v2)], then  U   o   =|X−Y|   
       Else  U   o   =Tv 1( X )− Tv 2( Y ) 
       If U o &gt;v2, then U o =v2 (only applicable to Gcd≠1)  Eq. 15         wherein:       
     
       
         
           
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 Definitions of Variables for Eq. 13 to Eq. 16 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 Tv1(X) 
                 Duration of a Type 2 PSC X 
               
               
                 Tv2(Y) 
                 Duration of a Type 2 PSC Y 
               
               
                 Gcd(L, J) 
                 Greatest common divisor of L and J 
               
               
                 U O   
                 Difference between the start times of Tv1(X) and Tv2(Y) 
               
               
                 X 
                 Sleep window of Tv1(X) 
               
               
                 Y 
                 Sleep window of Tv2(Y) 
               
               
                 v1 
                 Listening window of Tv1(X) 
               
               
                 v2 
                 Listening window of Tv2(Y) 
               
               
                   
               
            
           
         
       
     
     Eq. 12. shows that when the Gcd is equal to the second Type 2 PSC, Tv2(Y), or the two Type 2 PSCs have the same length, then the two Type 2 PSCs are started at the same time. Because the listening windows will be at the end of each of the Type 2 PSCs, the minimum availability interval is created when the overlap of the two listening windows is maximized. 
     Eq. 13 shows that when the Gcd is equal to one, the sleep window X is greater than the sleep window Y, and the listening window v2 is greater than the listening window v1, the alignment is set such that the start time Uo is equal to the sleep window X minus the sleep window Y. The start of the listening windows of the two Type 2 PSCs will be aligned in the first round. The two Type 2 PSC will line up once per cycle, because the sleep window X is greater than the sleep window Y, and the listening window v2 is greater than the listening window v1. If the Gcd is equal to one, the sleep window X is greater than the sleep window Y, but if the listening window v2 is less than or equal to the listening window v1, the alignment is set such that the start time Uo is equal to the length of PSC Tv1 (X) minus the length of PSC Tv2(Y). As discussed previously, a cycle is the duration before two Type 2 PSCs repeat the same spatial relationship with respect to each other. A round is every translation of X which equals Tv1(X). In other words, a cycle is composed of Ntx rounds of Tv1(X) and Nty rounds of Tv2(Y). 
     In Eq. 13, if the listening window v2 is greater than the listening window v1, aligning the starts of the listening windows v1 and v2 in the first round will “shift” small unavailability intervals that would fall at the beginning of the cycle (first rounds), if the start of the two Type 2 PSCs were aligned, and locate them in later rounds in the cycle. This will also reduce the length of the availability intervals in the first two rounds and improve the distribution of the unavailability intervals for almost half the cycle. If the start of the two Type 2 PSCs were aligned, small unavailability intervals may occur at the start of the cycle and the availability intervals will be longer in the first rounds, compared to aligning the starts of the listening windows v1 and v2 in the first round. In other words, aligning the ends of listening windows does not meet the condition of alignment discussed above, such as placing the longer unavailability intervals at the start of a cycle to provide more consistent unavailability intervals, and avoiding long availability intervals both at the start of and during a cycle to improve unavailability intervals when three or more PSCs are aligned. 
     In Eq. 13, if the listening window v2 is less than or equal to the listening window v1, aligning the ends of the listening windows v1 and v2 in the first round will reduce the duration of the unavailability intervals in the first two rounds of a cycle, and “shift” small unavailability intervals that would normally fall at the beginning of the cycle, and locate them in later rounds in the cycle. The duration and distribution of the unavailability intervals is improved for almost half of the cycle length. In other words, aligning the starts of the listening windows v1 and v2 in the first round does not meet the condition of alignment discussed above, such as placing the longer unavailability intervals at the start of a cycle to provide more consistent unavailability intervals, and avoiding long availability intervals both at the start of and during a cycle to improve unavailability intervals when three or more PSCs are aligned. When Gcd is equal to one, a trade-off is made between decreasing the total amount of unavailability (when Uo&gt;v2) compared to when Uo=0 and improving the distribution of unavailability intervals and decreasing the availability intervals in the first two rounds. 
     Eq. 14 shows that when the Gcd is equal to one, and the sleep window X is less than or equal to the sleep window Y, the alignment is set such that the start time Uo is equal to the length of PSC Tv1(X) minus the length of PSC Tv2(Y). When the Gcd is equal to one, and the sleep window X is less than the sleep window Y, the listening window v2 is less than the listening window v1. The listening window v2 is less than the listening window v1 to insure the length of PSC Tv1(X) is not greater than the length of PSC Tv2(Y). The ends of the listening windows of the two Type 2 PSCs will be aligned in the first round. In Eq. 14, aligning the ends of the listening windows v1 and v2 in the first round will reduce the duration of the unavailability intervals in the first two rounds of a cycle. The duration and distribution of the unavailability intervals is improved for almost half of the cycle length. In other words, aligning the starts of the listening windows v1 and v2 in the first round does not meet the condition of alignment discussed above, such as placing the longer unavailability intervals at the start of a cycle to provide more consistent unavailability intervals, and avoiding long availability intervals both at the start of and during a cycle to improve unavailability intervals when three or more PSCs are aligned. When Gcd is equal to one, a trade-off is made between decreasing the total amount of unavailability (when Uo&gt;v2) compared to when Uo=0 and improving the distribution of unavailability intervals and decreasing the availability intervals in the two first rounds. 
     Eq. 15 covers all other cases not covered in Eqs. 12, 13, and 14, that is, when the Gcd is not equal to one or the length of Tv2(Y). If Tv1 (X) is greater than Tv2(Y), the Gcd cannot be greater than Tv2(Y). If the Gcd is not equal to one or the length of Tv2(Y) and the sleep window X is greater than the sleep window Y, then the alignment is set such that the start time Uo is equal to the absolute value of the sleep window X minus the sleep window Y. The start of the listening windows of the two Type 2 PSCs will be aligned in the first round. Likewise, if the sleep window Y is greater than the sleep window X and the listening window vl is greater than the listening window v2, then the alignment is set such that the start time Uo is equal to the absolute value of the sleep window X minus the sleep window Y. The start of the listening windows of the two Type 2 PSCs will be aligned in the first round. If the Gcd is not equal to one or the length of Tv2(Y), and none of the above subconditions are met, the alignment is to set the start time Uo equal to the length of PSC Tv1(X) minus the length of PSC Tv2(Y). The ends of the listening windows of the two Type 2 PSCs will be aligned in the first round. In both cases, as discussed above for Eq. 13, the decision to align on the start of the listening windows or align on the ends of the listening windows is based on providing alignment for the particular characteristics of the two Type 2 PSCs. 
     In general, when Gcd is not equal to one or the length of Tv2(Y), and the start time Uo is greater than the listening window v2, the unavailability interval is decreased by the start time minus the listening window (Uo−v2) in the first cycle. When Uo&gt;v2, setting Uo=v2 represents a tradeoff between increasing the consistency of the unavailability intervals and the amount of availability intervals at the beginning of a cycle. If the start time Uo is not decreased by the start time minus the listening window, the total unavailability intervals are reduced, and the distribution and length of unavailability intervals in the cycle is not optimized. Except in the cases where the Gcd≠1, setting Uo=v2 does not reliably result in improved alignment. When Gcd=1 and Uo&gt;v2, not setting Uo=v2 represents a tradeoff between reducing the total unavailability intervals in the first cycle and a better distribution of the unavailability intervals at the beginning of future cycles. The next cycle will start with a small unavailability interval of Uo−v2 length, but will be followed by a more distributed pattern of unavailability intervals. 
       FIG. 8  shows a flow chart  800  illustrating an exemplary method to align three or more Type 2 PSCs. Alignment of multiple Type 2 PSCs  800  is used to produce an alignment of three or more Type 2 PSCs. 
     Step  802  sorts the Type 2 PSCs in order of decreasing duration. In other words, the shortest Type 2 PSC will be last on the list, and the longest Type 2 PSC will be first on the list. The Type 2 PSCs are sorted in order of decreasing respective durations in ranked pairs. As a result, for example, the longest Type 2 PSC is paired with the second longest Type 2 PSC to make the first Type 2 PSC ranked pair, the second longest Type 2 PSC is paired with the third longest Type 2 PSC to make the second Type 2 PSC ranked pair, etc. For example, if Tv1(X)=16 frames, Tv2(Y)=12 frames, and Tv3(Z)=9 frames, the order of decreasing duration would be Tv1(X), Tv2(Y), and Tv3(Z). Two Type 2 PSC ranked pairs would be made. The first Type 2 PSC ranked pair would be composed of Tv1(X) and Tv2(Y). The second Type 2 PSC ranked pair would be composed of Tv2(Y) and Tv3(Z). 
     Step  804  calculates the Gcd for each Type 2 PSC ranked pair in step  802 . In other words, there should be one less Gcd than the total number of Type 2 PSCs. Continuing the example, if Tv1(X)=16 frames, Tv2(Y)=12 frames, and Tv3(Z)=9 frames, then 2 Gcds would be calculated, Gcd(Tv1(X), Tv2(Y)) and Gcd(Tv2(Y), Tv3(Z)). The Gcd(Tv1(X), Tv2(Y)) is equal to 4 frames and the Gcd(Tv2(Y), Tv3(Z)) is equal to 3 frames. 
     Step  806  calculates the number of rounds, Nti and Ntj, for each Type 2 PSC ranked pair. The number of rounds is calculated from the Gcd for each Type 2 PSC ranked pair. In other words, the number of rounds Nti and Ntj for each Type 2 PSC ranked pair to complete a cycle of the Type 2 PSC ranked pair is calculated, as described earlier in connection with aligning two Type 2 PSCs. Continuing the example, where Tv1(X)=16 frames, Tv2(Y)=12 frames, and Tv3(Z)=9 frames, and Gcd(Tv1(X), Tv2(Y))=4 frames and Gcd(Tv2(Y), Tv3(Z))=3 frames, the numbers of rounds for the Type 2 PSC ranked pair composed of Tv1(X) and Tv2(Y) are Ntx=12/4=3 rounds and Nty=16/4=4 rounds. Likewise, the numbers of rounds for the Type 2 PSC ranked pair composed of Tv2(Y) and Tv3(Z) are Nty=9/3=3 rounds and Ntz=12/3=4 rounds. 
     Step  808  calculates the start times for each Type 2 PSC ranked pair. In other words, for each Type 2 PSC ranked pair, a Uo is determined based on Eqs. 12 to 15. Continuing the example, Tv1(X)=16 frames, Tv2(Y)=12 frames, Tv3(Z)=9 frames. X=11 frames, v1=5 frames, Y=8 frames, v2=4 frames, Z=6 frames and v3=3 frames. To calculate the Uo for the Type 2 PSC ranked pair composed of Tv1(X) and Tv2(Y), Eq. 15 is applied to determine that Uo xy =3 frames (|X−Y|=&gt;11−8=3 which is smaller than v2=4). To calculate the Uo for the Type 2 PSC ranked pair composed of Tv2(Y) and Tv3(Z), Eq. 15 is applied to determine that Uo yz =2 frames (from |X−Y|=&gt;8−6=2 which is smaller than v3=3). 
     In step  810 , the Uo is applied to the shortest member of each Type 2 PSC ranked pair, in succession, from longest to shortest, or from shortest to longest, or in any other logical order. In other words, the longer Type 2 PSC will start first, followed by the shorter Type 2 PSC. Continuing the example, where Tv1(X)=16 frames, Tv2(Y)=12 frames, Tv3(Z)=9 frames, Uo xy =3 frames, and Uo yz =2 frames, Tv1(X) will start at time 0, Tv2(Y) will start at 0+Uo xy , (e.g., 0+3 frames), and Tv3(Z) will start after Tv2(Y), at 0+Uo yz , +Uo xy  (e.g., 0+5 frames). It does not matter for the final result in which order the Uo are applied, as long as Uo for each Type 2 PSC ranked pair is applied to the shorter member of each Type 2 PSC ranked pair. 
       FIG. 9   a  is an exemplary diagram including a horizontal time axis, illustrating availability and unavailability intervals of a mobile device, e.g., MS  130 , based on sleep and listening windows of five Type 1 PSCs that are aligned by initial sleep window start time.  FIG. 9   b  is an exemplary diagram including a horizontal time axis, illustrating availability and unavailability intervals of a mobile device, e.g., MS  130 , based on sleep and listening windows of five Type 1 PSCs that are aligned. As shown in  FIGS. 9   a  and  9   b , a Type 1 PSC has a fixed length listening window alternating with sleep windows, where each sleep window is twice the size of the previous sleep window, up to some maximum sleep window size. In a Type 1 PSC, the initial (or first) sleep window is longer than or equal to the fixed length listening window. The lengths of Type 1 PSCs, Type 1 PSC listening windows, and Type 1 PSC sleep windows may be measured in frames. Generally, the number of Type 1 PSCs are expected to be relatively small as compared to the number of Type 2 PSCs, and after the first few rounds, their sleep windows are expected to be long compared to their listening windows. Type 1 PSCs are composed primarily of BE and NRT-VR connections. As shown in  FIGS. 9   a  and  9   b , for one Type 1 PSC, the initial sleep window is called SlpInit1 for PSC-T 1 - 1 , SlpInit2 for PSC-T 1 - 2 , etc. It will be assumed for a pair of Type 1 PSCs, the initial sleep window of PSC-T 1 - 1  is greater than or equal to the initial sleep window of PSC-T 1 - 2 , as shown below in Eq. 16. A Type 1 PSC listening window can be represented as vT1 1 . For PSC-T 1 - 1 , the listening window is vT1 1 , and for PSC-T 1 - 2  the listening window is vT1 2 . 
       SlpInit1≧SlpInit2  Eq. 16         wherein: SlpInit1 is the initial sleep window of a Type 1 PSC, PSC-T 1 - 1 
           SlpInit2 is the initial sleep window of a Type 1 PSC, PSC-T 1 - 2     
               
     One set of alignment rules for two Type 1 PSC is as follows: 
       If  SlpInit 1/ SlpInit 2=2, then  U   o   =To+SlpInit 2 +vT 1 2   Eq. 17 
       If  SlpInit 1/ SlpInit 2≠2 and  SlpInit 1− SlpInit 2=Odd, 
       then  U   o   =SlpInit 1 −SlpInit 2  Eq. 18 
       If  SlpInit 1/SlpInit2≠2 and  SlpInit 1 SlpInit 2=Even, then U o =0  Eq. 19         wherein:       
     
       
         
           
               
             
               
                 TABLE 3 
               
               
                   
               
               
                 Definitions of Variables for Eq. 17 to Eq. 19 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 SlpInit1 
                 Initial sleep window of a Type 1 PSC, PSC-T1-1 
               
               
                 SlpInit2 
                 Initial sleep window of a Type 1 PSC, PSC-T1-2 
               
               
                 U O   
                 Difference between the start times of PSC-T1-1 and PSC-T1-2 
               
               
                 To 
                 Start time of a Type 1 PSC, PSC-T1-1 
               
               
                 vT1 2   
                 Listening window of a Type 1 PSC, PSC-T1-2 
               
               
                   
               
            
           
         
       
     
     In Eq. 17, when SlpInit1 divided by SlpInit2 equals 2, the first initial sleep window is twice the length of the second initial sleep window. To optimize the alignment of two Type 1 PSCs with this relationship, the start time Uo of the first initial sleep window is set to when the second initial sleep window of Type 1 PSC is ready to start its second sleep window, which is equal to the first initial sleep window (SlpInit1=2*SlpInit2). In  FIG. 9   b , PSC-T 1 - 3  SlpInit3 is twice the length of PSC-T 1 - 5  SlpInit5, so that the PSC-T 1 - 3  start time would be after the start time of PSC-T 1 - 5  by SlpInit5 plus the listening window of PSC-T 1 - 5  (vT1 5 ). 
     In Eq. 18, when SlpInit1 divided by SlpInit2 does not equal 2, and SlpInit1 minus SlpInit2 is an odd number of frames, the Type 1 PSC with the shorter SlpInit is started after SlpInit1 minus SlpInit2 frames. In  FIG. 9   b , PSC-T 1 - 4  SlpInit4 is not twice the length of PSC-T 1 - 5  SlpInit5, and SlpInit4 minus SlpInit5 is an odd number of frames (3-2). Therefore, applying Eq. 18, PSC-T 1 - 5  is started at SlpInit4 minus SlpInit5, that is, one frame (3-2) after PSC-T 1 - 4 . 
     In Eq. 19, when SlpInit1 divided by SlpInit2 does not equal 2, and SlpInit1 minus SlpInit2 is an even number of frames, both Type 1 PSCs are started at the same time. In  FIG. 9   b , PSC-T 1 - 1  SlpInit1 is not twice the duration of PSC-T 1 - 2 , and SlpInit1 minus SlpInit2 is an even number of frames (7-5). Therefore, applying Eq. 19, PSC-T 1 - 1  and PSC-T 1 - 2  are started at the same time. 
       FIG. 10  shows a flow chart  1000  illustrating an exemplary set of steps to align three or more Type 1 PSCs. To align three or more Type 1 PSCs, the following method may be used to produce an alignment of multiple Type 1 PSCs as illustrated in  FIG. 9   b.    
     Step  1002  sorts the Type 1 PSCs in order of increasing duration of their initial sleep window. In other words, the Type 1 PSC with the shortest initial sleep window will be first on the list, and the Type 1 PSC with the longest initial sleep window will be last on the list. The sorting of the Type 1 PSCs further includes sorting in order of increasing respective durations in ranked pairs, the shortest Type 1 PSC paired with the second shortest Type 1 PSC to make a first Type 1 PSC ranked pair, the second shortest Type 1 PSC paired with the third shortest Type 1 PSC to make a second Type 1 PSC ranked pair, etc. In an example, it is assumed that SlpInit1 through SlpInit5 are the initial sleep windows of Type 1 PSCs PSC-T 1 - 1  through PSC-T 1 - 5 , respectively. If SlpInit1=7 frames, SlpInit2=5 frames, SlpInit3=4 frames, SlpInit4=3 frames, and SlpInit5=2 frames, then the order of Type 1 PSCs would be PSC-T 1 - 5 , PSC-T 1 - 4 , PSC-T 1 - 3 , PSC-T 1 - 2 , and PSC-T 1 - 1 . Further, four Type 1 PSC ranked pairs would be made. The first Type 1 PSC ranked pair would be composed of PSC-T 1 - 5  and PSC-T 1 - 4 . The second Type 1 PSC ranked pair would be composed of PSC-T 1 - 4  and PSC-T 1 - 3 . The third Type 1 PSC ranked pair would be composed of PSC-T 1 - 3  and PSC-T 1 - 2 . The fourth Type 1 PSC ranked pair would be composed of PSC-T 1 - 2  and PSC-T 1 - 1 . 
     Step  1004  applies Eq. 17 to all combinations of Type 1 PSCs for which the first initial sleep window is twice the length of the second initial sleep window. When two Type 1 PSCs have a relationship in which the first initial sleep window is twice the length of the second initial sleep window, the two Type 1 PSCs will be called a Type 1 PSC twice length pair. The start times of each Type 1 PSC twice length pair are fixed between the members of that Type 1 PSC twice length pair. Continuing the example, if SlpInit1=7 frames, SlpInit2=5 frames, SlpInit3=4 frames, SlpInit4=3 frames, and SlpInit5=2 frames, then SlpInit3 divided by SlpInit5 equals 2. Therefore, PSC-T 1 - 3  and PSC-T 1 - 5  are designated a Type 1 PSC twice length pair. Eq. 17 is applied to only the Type 1 PSC twice length pair of PSC-T 1 - 3  and PSC-T 1 - 5 , where PSC-T 1 - 5  has the shorter of the initial sleep windows. As shown in  FIG. 9   b , SlpInit3 is twice the length of SlpInit5. Thus, PSC-T 1 - 3  would start after PSC-T 1 - 5 , i.e., after a time period equal to SlpInit5 plus the listening window of PSC-T 1 - 5 . The relationship between the start times of PSC-T 1 - 3  and PSC-T 1 - 5  is thereby fixed. 
     In step  1006  the rules of Eq. 18 and 19 would be applied to Type 1 PSC ranked pair by Type 1 PSC ranked pair, in the order established in step  1002 . Where a relationship has already been established between a Type 1 PSC twice length pair, the operation of step  1006  would not alter that relationship. In other words, all Type 1 PSC ranked pairs are aligned according to Eq. 18 or 19 except when the longer SlpInit of the Type 1 PSC ranked pair&#39;s position was already set in Step  1004  to a Type 1 PSC whose position has been set in relation to the shorter SlpInit of the Type 1 PSC ranked pair&#39;s position. 
     Continuing the example in which SlpInit1=7 frames, SlpInit2=5 frames, SlpInit3=4 frames, SlpInit4=3 frames, and SlpInit5 =2 frames, SlpInit4 minus SlpInit5 equals 1 frame. Applying Eq. 18, since 1 is an odd number, PSC-T 1 - 5  will start 1 frame after PSC-T 1 - 4 . Considering next the pair PSC-T 1 - 4  and PSC-T 1 - 3 , where the relationship between PSC-T 1 - 5  and PSC-T 1 - 4  has been set, in step  1004 , the relationship between PSC-T 1 - 5  and PSC-T 1 - 3  has been set, the relationship between PSC-T 1 - 4  and PSC-T 1 - 3  is known. Assuming the listening windows of all the Type 1 PSCs are 2 frames in duration, Eq. 17 only applies to the pair of PSC-T 1 - 5  and PSC-T 1 - 3 , where PSC-T 1 - 5  is the shorter of the initial sleep windows. PSC-T 1 - 3  will start 4 frames after PSC-T 1 - 5 , and PSC-T 1 - 3  will start 5 frames after PSC-T 1 - 4 . Turning to the next Type 1 PSC pair, PSC-T 1 - 3  and PSC-T 1 - 2 , SlpInit2 minus SlpInit 3 equals 1. Applying Eq. 18, since 1 is an odd number, PSC-T 1 - 3  will start 1 frame after PSC-T 1 - 2 , and PSC-T 1 - 2  will start 3 frames after PSC-T 1 - 5  and 4 frames after PSC-T 1 - 4 . Turning to the last Type 1 PSC pair, PSC-T 1 - 2  and PSC-T 1 - 1 , SlpInit1 minus SlpInt2 equals 2. Applying Eq. 19, since 2 is an even number, PSC-T 1 - 1  and PSC-T 1 - 2  will start at the same time. 
       FIG. 11  is an exemplary diagram including a horizontal time axis, illustrating availability and unavailability intervals of a mobile device, e.g., MS  130 , based on sleep and listening windows of multiple PSCs with different Types that are aligned. As shown in  FIG. 11 , when more than one Type of PSC is present on a device, those PSCs can be aligned. 
       FIG. 12  is a flow chart  1200  illustrating an exemplary method to align multiple PSCs with different types. The exemplary method of flow chart  1200  may be used to align multiple PSCs. 
     In Step  1202 , each type of PSC is aligned within its own type of PSC. In other words, all Type 1 PSCs are aligned using, for example, the method disclosed above in connection with  FIG. 10 . Likewise, all Type 2 PSCs are aligned using, for example, the method disclosed above, in connection with  FIG. 8 . 
     In Step  1204 , the shortest Type 2 PSC and the last to start Type 1 PSC are aligned. The appropriate Eq. of the group of Eqs. 20, 21, 22, or 23 below is applied to align the shortest Type 2 PSC and the last to start Type 1 PSC. 
       If X&gt;SlpInit1 and v1&gt;vT1 1 , then U o(Type1)   X−SlpInit 1  Eq. 20. 
       If SlpInit1&gt;X and vT1 1 &gt;v1, then  U   o(Type2)   =SlpInit 1 −X   Eq. 21. 
       If X≧SlpInit1 and vT1 1 ≧v1, then start both PSCs at the same time  Eq. 22. 
       If (X=SlpInit1 and v1&gt;vT1 1 ) or (SlpInit1&gt;X and v1≧vT1 1 ), then the PSC with the shortest length has a  Uo=|Tv 1( X )−PSC- T 1-1|  Eq. 23.         wherein:       
     
       
         
           
               
             
               
                 TABLE 4 
               
               
                   
               
               
                 Definitions of Variables for Eq. 20 to Eq. 23 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 X 
                 Sleep window of the shortest Type 2 PSC, Tv1(X) 
               
               
                 SlpInit1 
                 Initial sleep window of a Type 1 PSC, PSC-T1-1 
               
               
                 v1 
                 Listening window of the shortest Type 2 PSC, Tv1(X) 
               
               
                 vT1 1   
                 Listening window of a Type 1 PSC, PSC-T1-1 
               
               
                 U O   
                 Difference between the start times of PSC-T1-1 and Tv1(X) 
               
               
                 Tv1(X) 
                 Duration of a Type 2 PSC = X + v1 
               
               
                 PSC-T1-1 
                 Duration of a Type 1 PSC, PSC-T1-1 
               
               
                   
               
            
           
         
       
     
     Applying Eqs. 20 and 21, if the duration of the sleep window of one of the two types of PSCs is greater than the duration of the sleep window of the other type of PSC and the duration of the listening window of the PSC with greater sleep window is also greater than the duration of the listening window of the other type of PSC, then the shortest duration PSC will be started at a time equal to their sleep windows difference (sleep window-initial sleep window or vice versa) to align the beginning of their listening windows. In other words, if the duration of both the initial sleep window and listening window of the Type 1 PSC are greater than the respective durations of the sleep window and listening window of Type 2 PSC, or the duration of both the sleep window and listening window of Type 2 PSC are greater than the respective durations of the initial sleep window and listening window of the Type 1 PSC, then align the start of their listening windows. The start of the listening windows are aligned by taking the difference between the absolute value of the Type 2 PSC sleep window minus the initial sleep window of the Type 1 PSC, and adding that difference to the start time of the shorter type of PSC. 
     Applying Eq. 22, if the duration of the sleep window of the Type 2 PSC is greater than or equal to the duration of the sleep window of the Type 1 PSC and the duration of the Type 2 PSC listening window is less than or equal to the duration of the listening window of the Type 1 PSC, then both PSCs will be started at the same time. Because the sleep window of a Type 1 PSC doubles every round, the availability intervals will be evenly distributed and there will be more opportunities to improve the unavailability intervals. 
     Using Eq. 23, if among the Type 1 and Type 2 PSCs, none of the conditions of Eqs. 20, 21, or 22 have been met, then the shortest duration PSC is started at a time equal the difference of the two PSCs lengths (sleep+listen) to align the end of the two PSCs listening windows. In other words, if the duration of the sleep window of the Type 2 PSC and the duration of the initial sleep window of the Type 1 PSC are equal, and the duration of the listening window of the Type 2 PSC is greater than the duration of the listening window of the Type 1 PSC, or the duration of the initial sleep window of the Type 1 PSC is greater than the duration of the sleep window of the Type 2 PSC, and the duration of the listening window of the Type 2 PSC is greater than or equal to the duration of the listening window of the Type 1 PSC, then the ends of their listening windows will be aligned. More particularly, the ends of their listening windows are aligned by taking the difference between the absolute value of the Type 2 PSC duration minus the Type 1 PSC duration, and adding that difference to the start time of the shorter PSC. 
     In Step  1206 , as shown in  FIG. 12 , any Type 3 PSCs may be aligned by matching the start time of the Type 3 PSC with the start time of the last to start PSC. The PSC may be either the last to start Type 1 PSC or the Type 2 PSC with the shortest duration. The Type 3 PSC will be aligned and have the same start time with one of the PSCs that has already been aligned. If the Type 3 PSC is aligned with a Type 2 PSC, the Type 3 PSC will be aligned with the PSC having the shortest duration. If the Type 3 PSC is aligned with a Type 1 PSC, the Type 3 PSC will be aligned with the PSC having the latest start time. 
       FIGS. 13-18  illustrate exemplary situations in which Step  1204  and Eqs. 20-23 are applied to the last to start Type 1 PSC, which may have various durations, and a Type 2 PSC with the shortest duration. 
       FIG. 13  is an exemplary diagram including a horizontal time axis, illustrating available and unavailable intervals of a mobile device, e.g., MS  130 , based on sleep and listening windows of multiple PSCs. In particular,  FIG. 13  shows a case in which the initial sleep window of the Type 1 PSC, PSC-T 1 - 1 , is greater than the sleep window of the Type 2 PSC, PSC-T 2 - 1 . The listening window of PSC-T 1 - 1  is greater than the listening window of PSC-T 2 - 1 . Applying step  1204 , Eq. 21 is used to determine that Uo, the delay in starting PSC-T 2 - 1 , is equal to the difference between the initial sleep window of PSC-T 1 - 1  and the sleep window of PSC-T 2 - 1 . The start of the listening windows of PSC-T 1 - 1  and PSC-T 2 - 1  will begin at the same time. In this manner, the two PSCs are aligned. 
       FIG. 14  is an exemplary diagram including a horizontal time axis, illustrating available and unavailable intervals of a mobile device, e.g., MS  130 , based on sleep and listening windows of multiple PSCs. In particular,  FIG. 14  shows a case in which the sleep window of the Type 2 PSC, PSC-T 2 - 1 , is greater than the initial sleep window of the Type 1 PSC, PSC-T 2 - 1 . The listening window of PSC-T 2 - 1  is greater than the listening window of PSC-T 1 - 1 . Applying step  1204 , Eq. 20 is used to determine that Uo, the delay in starting PSC-T 1 - 1 , is equal to the difference between the sleep window of PSC-T 2 - 1  and the initial sleep window of PSC-T 1 - 1 . The listening windows of the PSC-T 1 - 1  and PSC-T 2 - 1  will start at the same time. In this manner, the two PSCs are aligned. 
       FIG. 15  is an exemplary diagram including a horizontal time axis, illustrating available and unavailable intervals of a mobile device, e.g., MS  130 , based on sleep and listening windows of multiple PSCs. In particular,  FIG. 15  shows a case in which the sleep window of the Type 2 PSC, PSC-T 2 - 1 , is greater than or equal to the initial sleep window of the Type 1 PSC, PSC-T 1 - 1 . The listening window of PSC-T 1 - 1  is greater than the listening window of PSC-T 2 - 1 . Applying step  1204 , Eq. 22 is used to determine that PSC-T 1 - 1  and PSC-T 2 - 1  are started at the same time, and the two PSCs are aligned. 
       FIG. 16  is an exemplary diagram including a horizontal time axis, illustrating available and unavailable intervals of a mobile device, e.g., MS  130 , based on sleep and listening windows of multiple PSCs. In particular,  FIG. 16  shows a case in which the sleep window of the Type 2 PSC, PSC-T 2 - 1 , is greater than or equal to the initial sleep window of the Type 1 PSC, PSC-T 1 - 1 . The listening window of PSC-T 1 - 1  is equal to the listening window of PSC-T 2 - 1 . Applying step  1204 , Eq. 22 is used to determine that PSC-T 1 - 1  and PSC-T 2 - 1  are started at the same time, and the two PSCs are aligned. 
       FIG. 17  is an exemplary diagram including a horizontal time axis, illustrating available and unavailable intervals of a mobile device, e.g., MS  130 , based on sleep and listening windows of multiple PSCs. In particular,  FIG. 17  shows a case in which the initial sleep window of the Type 1 PSC, PSC-T 1 - 1 , is greater than or equal to the sleep window of the Type 2 PSC, PSC-T 2 - 1 . The listening window of PSC-T 2 - 1  is greater than the listening window of PSC-T 1 - 1 . Applying step  1204 , Eq. 23 is used to determine that Uo, the delay in starting PSC-T 2 - 1 , is equal to the difference between the PSC-T 1 - 1  length (sleep+listen) and the PSC-T 2 - 1  length (sleep+listen). The listening windows of PSC-T 1 - 1  and PSC-T 2 - 1  will end at the same time, and the two PSCs are aligned. 
       FIG. 18  is an exemplary diagram including a horizontal time axis, illustrating available and unavailable intervals of a mobile device, e.g., MS  130 , based on sleep and listening windows of multiple PSCs. In particular,  FIG. 18  shows a case in which the initial sleep window of the Type 1 PSC, PSC-T 1 - 1 , is greater than the sleep window of the Type 2 PSC, PSC-T 2 - 1 . The listening window of PSC-T 2 - 1  is equal to the listening window of PSC-T 1 - 1 . Applying step  1204 , Eq. 23 is used to determine that Uo, the delay in starting PSC-T 2 - 1 , is equal to the difference between the PSC-T 1 - 1  length (sleep+listen) and the PSC-T 2 - 1  length (sleep+listen). The listening windows of PSC-T 1 - 1  and PSC-T 2 - 1  will end at the same time, and the two PSCs are aligned. 
     Once the PSCs have been aligned, the plurality of PSCs, each associated power savings window size, the aligned PSCs, and the relative start times between PSCs, may be communicated to BS  110 . In another exemplary embodiment, MS  130  may manage its own power management, and not communicate the plurality of PSCs, each associated power savings window size, the aligned PSCs, and the relative start times between PSCs, to BS  110 . In a further exemplary embodiment, only the plurality of PSCs and each associated power savings window size may be communicated to BS  110 . 
     It will be apparent to those skilled in the art that various modifications and variations can be made in the system and method for power savings in a wireless communications network. It is intended that the standard and examples be considered as exemplary only, with a true scope of the disclosed embodiments being indicated by the following claims and their equivalents.