Abstract:
A technique for time tracking helps a mobile communication device with multiple SIMs to more accurately maintain synchronization with a base station. By utilizing synchronization information from both SIMs, the technique is able to more frequently and more accurately adjust timing information for each SIM. As a result, the mobile communication device exhibits an increased ability to accurately synchronize without the need for a higher precision reference or increased power consumption.

Description:
1. PRIORITY CLAIM 
     This application claims the benefit of priority to the following U.S. provisional patent applications: 
     U.S. Patent Application No. 61/569,621, filed 12 Dec. 2011; 
     U.S. Patent Application No. 61/587,521, filed 17 Jan. 2012; and 
     U.S. Patent Application No. 61/595,546, filed 6 Feb. 2012. 
    
    
     2. TECHNICAL FIELD 
     This disclosure relates to communication devices with multiple Subscriber Identity Modules (SIMs). The disclosure also relates to enhanced time tracking in communication devices with multiple SIMs. 
     3. BACKGROUND 
     Rapid advances in electronics and communication technologies, driven by immense customer demand, have resulted in the widespread adoption of mobile communication devices. The extent of the proliferation of such devices is readily apparent in view of some estimates that put the number of wireless subscriber connections in use around the world at nearly 80% of the world&#39;s population. Furthermore, other estimates indicate that (as just three examples) the United States, Italy, and the UK have more mobile phones in use in each country than there are people living in those countries. 
     Relatively recently, cellular phone manufactures have introduced phone designs that include multiple SIM cards. Each SIM card facilitates a separate connection to the same network or different networks. As a result, the SIMs provide the owner of the phone with, for example, two different phone numbers handled by the same phone hardware. Accordingly, the multiple SIM approach alleviates to some degree the need to carry different physical phones, and improvements in multiple SIM communication devices will continue to make such devices attractive options for the consumer. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The innovation may be better understood with reference to the following drawings and description. In the figures, like reference numerals designate corresponding parts throughout the different views. 
         FIG. 1  shows an example of user equipment with multiple SIMs. 
         FIG. 2  shows an example of a paging block and the bits of the paging block. 
         FIG. 3  shows an example of determining timing error using the paging block. 
         FIG. 4  shows an example of user equipment including multiple SIMS where the scheduled reception of paging blocks for each SIM may collide. 
         FIG. 5  shows an example an example of user equipment including multiple SIMS where the time tracking logic uses timing information from the paging blocks of SIM 1  to update the timing offset. 
         FIG. 6  shows an example an example of user equipment including multiple SIMS where the time tracking logic uses timing information from the paging blocks of SIM 1  and SIM 2  to update the timing offset. 
         FIG. 7  shows another example an example of user equipment including multiple SIMS where the time tracking logic uses timing information from the paging blocks of SIM 1  and SIM 2  to update the timing offset. 
         FIG. 8  shows another example an example of user equipment including multiple SIMS where the time tracking logic uses timing information from the paging blocks of SIM 1  to update the timing offset. 
         FIG. 9  shows an example an example of user equipment including multiple SIMS where the time tracking logic uses timing information from the paging blocks of SIM 1  and SIM 2  to update the timing offset. 
         FIG. 10  shows another example an example of user equipment including multiple SIMS where the time tracking logic uses timing information from the paging blocks of SIM 1  and SIM 2  to update the timing offset. 
         FIG. 11  shows an example of a flow diagram of time tracking logic that user equipment may implement in hardware, software, or both. 
     
    
    
     DETAILED DESCRIPTION 
     The discussion below makes reference to user equipment. User equipment may take many different forms and have many different functions. As one example, user equipment may be a cellular phone capable of making and receiving wireless phone calls. The user equipment may also be a smartphone that, in addition to making and receiving phone calls, runs general purpose applications. User equipment may be virtually any device that wirelessly connects to a network, including as additional examples a driver assistance module in a vehicle, an emergency transponder, a pager, a satellite television receiver, a networked stereo receiver, a computer system, music player, or virtually any other device. The discussion below addresses how to track symbol timing in user equipment that includes multiple (e.g., two) SIMs. 
       FIG. 1  shows an example of user equipment  100  with multiple SIMs, in this example the SIM 1   102  and the SIM 2   104 . An electrical and physical interface  106  connects SIM 1   102  to the rest of the user equipment hardware, for example, to the system bus  110 . Similarly, the electrical and physical interface  108  connects the SIM 2  to the system bus  110 . 
     The user equipment  100  includes a communication interface  112 , system logic  114 , and a user interface  118 . The system logic  114  may include any combination of hardware, software, firmware, or other logic. The system logic  114  may be implemented, for example, in a system on a chip (SoC), application specific integrated circuit (ASIC), or other circuitry. The system logic  114  is part of the implementation of any desired functionality in the user equipment. In that regard, the system logic  114  may include logic that facilitates, as examples, running applications, accepting user inputs, saving and retrieving application data, establishing, maintaining, and terminating cellular phone calls, wireless network connections, Bluetooth connections, or other connections, and displaying relevant information on the user interface  118 . The user interface  118  may include a graphical user interface, touch sensitive display, voice or facial recognition inputs, buttons, switches, and other user interface elements. 
     The communication interface  112  may include one or more transceivers. The transceivers may be wireless transceivers that include modulation/demodulation circuitry, amplifiers, analog to digital and digital to analog converters and/or other logic for transmitting and receiving through one or more antennas, or through a physical (e.g., wireline) medium. As one implementation example, the communication interface  112  and system logic  114  may include a BCM2091 EDGE/HSPA Multi-Mode, Multi-Band Cellular Transceiver and a BCM59056 advanced power management unit (PMU), controlled by a BCM28150 HSPA+ system-on-a-chip (SoC) baseband smartphone processer. These integrated circuits, as well as other hardware and software implementation options for the user equipment  100 , are available from Broadcom Corporation of Irvine Calif. 
     The transmitted and received signals may adhere to any of a diverse array of formats, protocols, modulations, frequency channels, bit rates, and encodings that presently or in the future support communications including paging notifications associated with SIMs. As one specific example, the communication interface  112  may support transmission and reception under the Universal Mobile Telecommunications System (UMTS). The techniques described below, however, are applicable to other communications technologies that include paging whether arising from the 3rd Generation Partnership Project (3GPP), GSM (R) Association, Long Term Evolution (LTE)™ efforts, or other partnerships or standards bodies. 
     In order for user equipment  100  to reliably transmit and receive data over a network, user equipment  100  may synchronize its internal timing with the timing of a base transceiver station (BTS) on the network. User equipment  100  may synchronize with the timing from a BTS of the network by aligning an internal time base  140  of the user equipment  100  with the timing information received from the BTS. In order to assist with synchronization, the BTS may periodically send timing information to the user equipment  100  so that the user equipment  100  can correct its internal time base  140 . In order to receive the timing information, the user equipment  100  may actively listen on the synchronization channel or may periodically listen on the paging channel. 
     The user equipment  100  may connect with a network in either active mode or idle mode. When user equipment  100  connects to a network in active mode, user equipment  100  is in frequent communication with the network and frequently receives timing information from the network. When the network connection is in idle mode, the user equipment  100  can remain in a reduced power “sleep” mode, “waking up” periodically to listen for synchronization information contained on the paging channel of the network. User equipment  100  may utilize multiple internal time bases, including, for example, an active mode time base  142  and an idle mode time base  144 . The active mode time base  142  may be more accurate than the idle mode time base  144 . The active mode time base  142  may be used while the user equipment is connected to a network in active mode and actively transmitting/receiving data. User equipment  100  may have an idle mode time base  144  that is used when user equipment  100  is connected to the network in idle mode and not actively transmitting/receiving data. User equipment  100  may use idle mode time base  142  to determine the particular time that user equipment  100  should wake up from sleep mode. Due to the fact that the active mode time base  142  may be more accurate and may consume additional power, the user equipment  100  may, while in sleep mode, power down the active mode time base  142 . 
     During periods when user equipment  100  is in sleep mode and does not receive timing information from the BTS, user equipment  100  may rely on its internal time base  140 . However, internal time base  140  may be inaccurate and may “drift” with respect to the timing of the BTS. The time drift may be due to phase error or frequency error with respect to the phase and/or frequency of the BTS. If user equipment  100  does not periodically wake up to listen for the synchronization information contained in the paging block from the network, the user equipment  100  may lose synchronization with the network. As a result, the user equipment  100  may not receive a paging indicator from the network and may miss a call, message, or data that the network has designated for the user equipment  100 . 
     When in idle mode, user equipment  100  may be scheduled to wake up at a specified interval to receive the synchronization information contained in the paging block from the network. The specified interval may be based on a background paging schedule (BPS). As one example of the background paging schedule, the network&#39;s discontinuous reception cycle (DRX) interval may be used as the background paging schedule. The BPS provides the length of time specified by the network during which the user equipment  100  remains asleep between periods of listening for the synchronization information contained in the paging block. The length of time for the BPS may vary, depending on the type of communication technology used (e.g., GSM, CDMA, UMTS, etc.) and the particular settings used by the particular service provider that operates the network. As one example for one network, the BPS may be 2 seconds, while for other networks, the BPS may be shorter or longer. 
     Synchronization information from the network may be contained in a paging block sent from the BTS to the user equipment  100  on the paging channel.  FIG. 2  shows an example of paging block  202 . Paging block  202  may contain bursts of data in the paging block. For example, the burst  210  is contained in the paging block  202 . Burst  210  includes data bits  212  and midamble  220 . The midamble is a known sequence of bits, such as a training sequence, that may be contained in each burst of paging block  202 . Midamble  220  can be used for synchronization because the midamble arrives at a known location within each burst. When the user equipment  100  identifies and locates the midamble, the user equipment  100  can identify the start position and/or stop position of the data burst. 
       FIG. 3  shows an example of using midamble  220  to determine a timing error  306 . The user equipment  100  may use its internal time base  140  to predict the arrival of midamble  220  at predicted arrival time  302 . Once the user equipment  100  identifies midamble  220 , the user equipment  100  identifies the actual arrival time  304  of midamble  220 . The time difference between the predicted arrival time  302  and actual arrival time  304  results in the timing error  306 . User equipment  100  may use timing error  306  to compensate the internal time base  140  when predicting the arrival time of the next paging block. 
     In order to predict the arrival time of the next paging block, user equipment  100  may use a time tracking loop. The time tracking loop may correct for the drift in the internal time base  140 . The time tracking loop may apply a correction factor to account for the timing drift of the internal time base  140 . The correction factor may be updated each time user equipment  100  receives a paging block and determines timing error  306  from the burst. 
     Where a user equipment has multiple SIMs for connecting to multiple networks, the user equipment may require synchronization with multiple BTS&#39;s on multiple networks. Each network (e.g., network  130  or  132 ) may supply its own timing information, and the BPS may have a different time period for each network. User equipment  100  may track the timing difference that may exist between the user equipment&#39;s internal time base  140  and the timing for each network. As a result, the user equipment  100  may apply a different correction factor for each network with which it is synchronized. As will be described in more detail below, user equipment  100  may use the timing information received from one network, either network, or both networks when tracking the timing correction factor for the user equipment  100 . 
     In some implementations, user equipment  100  may share radio frequency resources between multiple SIMs. As a result, both SIMs cannot simultaneously receive paging blocks from the network. Because both SIMs may not simultaneously receive paging blocks from the network, in situations, for example, where user equipment  100  is scheduled to receive a paging block from SIM 1  network  130  at the same time user equipment  100  is scheduled to be receive a paging block from SIM 2  network  132 , the paging blocks “collide.” When the paging blocks from multiple networks collide, user equipment  100  may choose whether to receive the paging block from SIM 1  network  130 , SIM 2  network  132 , or neither. As a result, one or both paging blocks may be ignored or lost. If user equipment  100  ignores or loses a paging block, user equipment may wait for the next scheduled paging block. 
       FIG. 4  shows an example of “collisions” between paging blocks from multiple networks. Timing graph  400  shows a schedule of paging blocks from SIM 1  network  130  and SIM 2  network  132  that are designated for user equipment  100 . Paging blocks  402 ,  404 , and  406  are scheduled by SIM 1  network  130  at BPS 1  time interval  401 . Paging blocks  412 ,  414 ,  416  are scheduled by SIM 2  network  132  at BPS 2  time interval  411 . Based on the schedule, paging block  402  and paging block  412  are scheduled to arrive at user equipment  100  in a partially overlapping manner, indicated by timing overlap  420 . Because paging block  402  and paging block  412  are scheduled to collide (i.e., overlap), user equipment  100  may choose to receive paging block  402 , paging block  412 , or neither. Similarly, paging block  404  and paging block  416  are scheduled to arrive at user equipment  100  at the same time, indicated by timing overlap  432 . Because paging block  404  and paging block  416  are scheduled to collide, user equipment  100  may choose to receive paging block  404 , paging block  416 , or neither. As a result of the collisions, user equipment  100  may lose opportunities to receive timing information from either SIM 1  network  130  or SIM 2  network  132 . When paging blocks collide and user equipment  100  waits for additional paging blocks, the internal time base may drift further out of synchronization with the network. As a result of lost paging blocks, user equipment  100  may not be able to update the timing correction factor as frequently as desired. Thus, the user equipment may lose synchronization between the user equipment  100  and network  130  or  132 . System logic  114  provides certain advantages. 
     In one implementation, the system logic  114  includes one or more processors  116  and a memory  120 . The memory  120  stores, for example, time tracking logic  122  that the processor  116  executes. The memory  120  may also store SIM 1  network timing information  124 , SIM 2  network timing information  126 , and time tracking parameters  128 . As will be described in more detail below, the time tracking logic  122  facilitates timing correction so that user equipment  100  can more accurately synchronize with each network, even when some paging blocks collide. 
     The time tracking logic  122  may independently track the drift of internal time base  140  for each network with which user equipment  100  is connected. The time tracking logic  122  may independently track the time base drift by having independent tracking loops for each network. For example, if user equipment  100  is connected in idle mode to SIM 1  network  130 , the time tracking logic  122  may use the timing error determined from paging blocks received from SIM 1  network  130 . Using the timing error from paging blocks received from SIM 1  network  130 , the time tracking logic  122  may apply an appropriate correction factor to the internal time base  140 . Similarly, if user equipment  100  is connected in idle mode to SIM 2  network  132 , the time tracking logic  122  may use the timing error determined from paging blocks received from SIM 2  network  132 . Using the timing error from paging blocks received from SIM 2  network  132 , the time tracking logic  122  may apply an appropriate correction factor to the internal time base  140 . 
     In another implementation, the time tracking logic  124  may track the drift of internal time base  140  by combining—into a single tracking loop—the timing error determined from paging blocks received from the multiple networks with which user equipment  100  may be connected. For example, if user equipment  100  is connected to SIM 1  network  130  and SIM 2  network  132 , the time tracking logic  122  may use the SIM 1  network paging blocks and SIM 2  network paging blocks in order to determine the appropriate time base compensation for synchronizing user equipment  100  with SIM 1  network  130  and SIM 2  network  132 . In particular, by combining the timing error determined from paging blocks received from multiple networks, the user equipment is able to take advantage of timing information received from both networks in order to more frequently update the timing compensation and more accurately synchronize the timing of the user equipment  100  to the timing of the network, even when some paging blocks collide and/or are lost. 
     The time tracking logic  122  may use certain time tracking parameters  128  in order to utilize timing error determined from paging blocks received from multiple networks for improved time tracking. The time tracking logic  122  may store the time tracking parameters  128  in memory  120  and update the time tracking parameters  128  as the processor  116  calculates and processes the timing information. For example, when user equipment  100  is in idle mode, each time a paging block is received from SIM 1  network  130  or SIM 2  network  132 , the time tracking logic  122  may update the time tracking parameters  128 . 
     In one implementation, example time tracking parameters  128  may include: 
     
       
         
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                   
                 Parameter 
                   
               
               
                 Variable 
                 Type 
                 Description 
               
               
                   
               
             
             
               
                 α 1   
                 constant 
                 Gain of the first order phase locked loop. 
               
               
                   
                   
                 This constant may be used to stabilize the 
               
               
                   
                   
                 loop and may be set to a rational number 
               
               
                   
                   
                 less than one 
               
               
                 α d   
                 constant 
                 Gain of the “delta loop.” This constant 
               
               
                   
                   
                 may be used to stabilize the loop and may 
               
               
                   
                   
                 be set to a rational number less than one 
               
               
                 n 
                 index 
                 An index representing receipt of the current 
               
               
                   
                   
                 paging block; n + 1 is the next scheduled 
               
               
                   
                   
                 paging block 
               
               
                 i(n) 
                 input 
                 Network Identification (e.g., SIM1 network 
               
               
                   
                   
                 or SIM2 network) for the n-th paging block 
               
               
                 ê(n) 
                 input 
                 The measured timing error from the n-th 
               
               
                   
                   
                 paging block 
               
               
                 c 
                 internal state 
                 First order loop filter output, representing 
               
               
                   
                 variable 
                 the timing adjustment due to phase error 
               
               
                 d 
                 internal state 
                 The differential adjustment applied when 
               
               
                   
                 variable 
                 the next scheduled paging block is from a 
               
               
                   
                   
                 different network 
               
               
                 δ 
                 internal 
                 Timing adjustment between the previous 
               
               
                   
                 variable 
                 paging block and the current paging block 
               
               
                   
               
             
          
         
       
     
     In one implementation, using the time tracking parameters  128  listed above, the time tracking logic  122  may implement the following algorithm: 
     
       
         
               
               
             
               
               
             
               
               
               
               
             
               
               
             
           
               
                   
                 TABLE 2 
               
               
                   
                   
               
             
             
               
                   
                 for n = 1,2, ... 
               
             
          
           
               
                   
                 % calculate loop filter output (phase error timing adjustment) 
               
               
                   
                 c = α 1 ê(n); 
               
               
                   
                 % update differential adjustment 
               
               
                   
                 d = d + (−1) i(n)  α d c; 
               
               
                   
                 % determine time base adjustment based on phase timing error 
               
             
          
           
               
                   
                 if 
                 i(n + 1) == i(n) 
                 then δ = c; 
               
               
                   
                 elseif 
                 i(n + 1) == 1 
                 then δ = c − d; 
               
               
                   
                 elseif 
                 i(n + 1) == 2 
                 then δ = c + d; 
               
             
          
           
               
                   
                 end 
               
               
                   
                   
               
             
          
         
       
     
       FIG. 5  shows an example timing graph  500  that includes a series of paging blocks from SIM 1  network  130  and SIM 2  network  132  that are scheduled for user equipment  100 . Because of radio frequency resource sharing, as described above, paging blocks  412 ,  414 ,  416 , and  418 , in this example, are lost due to collisions with paging blocks from SIM 1  network  130 . User equipment  100  may chose instead to receive paging blocks  402 ,  404 , and  406  from SIM 1  network  130 . Following timing graph  500  from left to right and using one implementation of time tracking logic  122 , user equipment  100  receives paging block  402 . Using the midamble of the burst, user equipment  100  determines the timing error between the expected arrival of the midamble and the actual arrival of the midamble of the burst, labeled ê 1 . Time tracking logic  122  uses timing error ê 1  and gain factor α 1  to determine the loop filter output c 1 . Time tracking logic  122  updates the differential adjustment factor, d 1 , subtracting the currently calculated loop filter output c 1  from the prior differential adjustment factor, d. Note that time tracking logic  122  subtracts c 1  from d 1  because user equipment  100  is currently listening to the network with network identification one (i.e., SIM 1  network  130 ). Time tracking logic  122  determines the timing adjustment, δ 1 , for the next scheduled paging block using the loop filter output c 1 . User equipment  100  may use timing adjustment, δ 1 , as the compensation factor to apply to internal time base  140  for predicting the expected arrival of the next paging block  404 . After user equipment  100  receives and processes paging block  402 , it may enter a sleep mode until the next paging block is scheduled to arrive. While in sleep mode, user equipment  100  may use its internal time base  140  along with timing adjustment, δ 2 , to predict the expected arrival of the next paging block  404 . 
     When user equipment  100  expects the next scheduled paging block  404 , user equipment wakes up from sleep mode to listen for paging block  404 . Again, using the midamble of the burst, user equipment  100  determines the timing error between the expected arrival of the midamble and the actual arrival of the midamble of the burst, labeled ê 2 . Time tracking logic  122  uses timing error ê 2  and gain factor α 1  to determine the loop filter output c 2 . Time tracking logic  122  updates the differential adjustment factor, d 2 , subtracting the currently calculated loop filter output c 2  from the prior differential adjustment factor, d 1 . Note that time tracking logic  122  subtracts c 2  from d 1  because user equipment  100  is currently listening to the network with network identification one (i.e., SIM 1  network  130 ). Time tracking logic  122  determines the timing adjustment, δ 2 , for the next scheduled paging block using the loop filter output c 2 . User equipment  100  may use timing adjustment, δ 2 , as the compensation factor to apply to internal time base  140  for predicting the expected arrival of the next paging block  406 . After user equipment  100  receives and processes paging block  404 , it may enter a sleep mode until the next paging block is scheduled to arrive. While in sleep mode, user equipment  100  may use its internal time base  140  along with timing adjustment, δ 2 , to predict the expected arrival of the next paging block  406 . 
     When user equipment  100  expects the next scheduled paging block  406 , user equipment wakes up from sleep mode to listen for paging block  406 . Again, using the midamble of the burst, user equipment  100  determines the timing error between the expected arrival of the midamble and the actual arrival of the midamble of the burst, labeled ê 3 . Time tracking logic  122  uses timing error ê 3  and gain factor α 1  to determine the loop filter output c 3 . Time tracking logic  122  updates the differential adjustment factor, d 3 , subtracting the currently calculated loop filter output c 3  from the prior differential adjustment factor, d 2 . Note that time tracking logic  122  subtracts c 3  from d 2  because user equipment  100  is currently listening to the network with network identification one (i.e., SIM 1  network  130 ). Because the timing adjustment, δ 3 , for the next scheduled paging block depends on whether the next scheduled paging block will be received on the same network or whether the paging block with be received from another network, the time tracking logic  122  may not determine the timing adjustment for the next paging block until user equipment  100  determines whether the next scheduled paging block will arrive from SIM 1  network  130  or SIM 2  network  132 . 
       FIG. 6  shows another example of how the user equipment  100  may use a similar series of paging blocks. Timing graph  600  includes a series of paging blocks from SIM 1  network  130  and SIM 2  network  132  that are scheduled for user equipment  100 . Because of radio frequency resource sharing, as described above, paging blocks  404 ,  406 , and  412 , in this example, are lost due to collisions between paging blocks from SIM 1  network  130  and SIM 2  network  132 . User equipment  100  may chose instead to receive paging blocks  402 ,  414 ,  416 , and  418 . Following timing graph  600  from left to right and using one implementation of time tracking logic  122 , user equipment  100  receives paging block  402 . Using the midamble of the burst, user equipment  100  determines the timing error between the expected arrival of the midamble and the actual arrival of the midamble of the burst, labeled ê 1 . Time tracking logic  122  uses timing error ê 1  and gain factor α 1  to determine the loop filter output c 1 . Time tracking logic  122  updates the differential adjustment factor, d 1 , subtracting the currently calculated loop filter output c 1  from the prior differential adjustment factor, d. Note that time tracking logic  122  subtracts c 1  from d because user equipment  100  is currently listening to the network with network identification one (i.e., SIM 1  network  130 ). Time tracking logic  122  determines the timing adjustment, δ 1 , for the next scheduled paging block using the loop filter output c 1  and adds the differential adjustment factor d 1 . Note that time tracking logic  122  adds d 1  because the currently received paging block  402  is from SIM 1  network  130  while the next scheduled paging block  414  is from SIM 2  network  132 . User equipment  100  may use timing adjustment, δ 1 , as the compensation factor to apply to internal time base  140  for predicting the expected arrival of the next paging block  414 . After user equipment  100  receives and processes paging block  402 , it may enter a sleep mode until the next paging block is scheduled to arrive. While in sleep mode, user equipment  100  may use its internal time base  140  along with timing adjustment, δ 1 , to predict the expected arrival of the next paging block  414 . 
     When user equipment  100  expects the next scheduled paging block  414 , user equipment wakes up from sleep mode to listen for paging block  414 . Again, using the midamble of the burst, user equipment  100  determines the timing error between the expected arrival of the midamble and the actual arrival of the midamble of the burst, labeled ê 2 . Time tracking logic  122  uses timing error ê 2  and gain factor α 1  to determine the loop filter output c 2 . Time tracking logic  122  updates the differential adjustment factor, d 2 , adding the currently calculated loop filter output c 2  and the prior differential adjustment factor, d 1 . Note that time tracking logic  122  adds c 2  and d 1  because user equipment  100  is currently listening to the network with network identification two (i.e., SIM 2  network  132 ). Time tracking logic  122  determines the timing adjustment, δ 2 , for the next scheduled paging block using the loop filter output c 2 . Note that time tracking logic  122  does not add or subtract d 2  because the currently received paging block  414  is from SIM 2  network  132  and the next scheduled paging block  416  is also from SIM 2  network  132 . User equipment  100  may use timing adjustment, δ 2 , as the compensation factor to apply to internal time base  140  for predicting the expected arrival of the next paging block  416 . After user equipment  100  receives and processes paging block  414 , it may enter a sleep mode until the next paging block is scheduled to arrive. While in sleep mode, user equipment  100  may use its internal time base  140  along with timing adjustment, δ 2 , to predict the expected arrival of the next paging block  416 . 
     When user equipment  100  expects the next scheduled paging block  416 , user equipment wakes up from sleep mode to listen for paging block  416 . Again, using the midamble of the burst, user equipment  100  determines the timing error between the expected arrival of the midamble and the actual arrival of the midamble of the burst, labeled ê 3 . Time tracking logic  122  uses timing error ê 3  and gain factor α 1  to determine the loop filter output c 3 . Time tracking logic  122  updates the differential adjustment factor, d 3 , adding the currently calculated loop filter output c 3  and the prior differential adjustment factor, d 2 . Note that time tracking logic  122  adds c 3  and d 2  because user equipment  100  is currently listening to network identification two (i.e., SIM 2  network  132 ). User equipment  100  may use timing adjustment, δ 3 , as the compensation factor to apply to internal time base  140  for predicting the expected arrival of the next paging block  418 . After user equipment  100  receives and processes paging block  416 , it may enter a sleep mode until the next paging block is scheduled to arrive. While in sleep mode, user equipment  100  may use its internal time base  140  along with timing adjustment, δ 3 , to predict the expected arrival of the next paging block  418 . 
     When user equipment  100  expects the next scheduled paging block  418 , user equipment wakes up from sleep mode to listen for paging block  418 . Again, using the midamble of the burst, user equipment  100  determines the timing error between the expected arrival of the midamble and the actual arrival of the midamble of the burst, labeled ê 4 . Time tracking logic  122  uses timing error ê 4  and gain factor α 1  to determine the loop filter output c 4 . Time tracking logic  122  updates the differential adjustment factor, d 4 , adding the currently calculated loop filter output c 4  and the prior differential adjustment factor, d 3 . Note that time tracking logic  122  adds c 4  and d 3  because user equipment  100  is currently listening to the network with network identification two (i.e., SIM 2  network  132 ). Because the timing adjustment, δ 4 , for the next scheduled paging block depends on whether the next scheduled paging block will be received on the same network or whether the paging block with be received from another network, the time tracking logic  122  may not determine the timing adjustment for the next paging block until user equipment  100  determines whether the next scheduled paging block will arrive from SIM 1  network  130  or SIM 2  network  132 . 
       FIG. 7  shows another example of how the user equipment  100  may use a similar series of paging blocks. Timing graph  700  includes a series of paging blocks from SIM 1  network  130  and SIM 2  network  132  that are scheduled for user equipment  100 . Because of radio frequency resource sharing, as described above, paging blocks  412 ,  416 , and  418 , in this example, are lost due to paging blocks collisions between paging blocks from SIM 1  network  130  and SIM 2  network  132 . User equipment  100  may chose instead to receive paging blocks  402 ,  414 ,  404 , and  406 . Following timing graph  700  from left to right and using one implementation of time tracking logic  122 , user equipment  100  receives paging block  402 . Using the midamble of the burst, user equipment  100  determines the timing error between the expected arrival of the midamble and the actual arrival of the midamble of the burst, labeled ê 1 . Time tracking logic  122  uses timing error ê 1  and gain factor α 1  to determine the loop filter output c 1 . Time tracking logic  122  updates the differential adjustment factor, d 1 , subtracting the currently calculated loop filter output c 1  from the prior differential adjustment factor, d. Note that time tracking logic  122  subtracts c 1  from d because user equipment  100  is currently listening to the network with network identification one (i.e., SIM 1  network  130 ). Time tracking logic  122  determines the timing adjustment, δ 1 , for the next scheduled paging block  414  using the loop filter output c 1  and adds the differential adjustment factor d 1 . Note that time tracking logic  122  adds d 1  because the currently received paging block  402  is from SIM 1  network  130  while the next scheduled paging block  414  is from SIM 2  network  132 . User equipment  100  may use timing adjustment, δ 1 , as the compensation factor to apply to internal time base  140  for predicting the expected arrival of the next paging block  414 . After user equipment  100  receives and processes paging block  402 , it may enter a sleep mode until the next paging block is scheduled to arrive. While in sleep mode, user equipment  100  may use its internal time base  140  along with timing adjustment, δ 1 , to predict the expected arrival of the next paging block  414 . 
     When user equipment  100  expects the next scheduled paging block  414 , user equipment wakes up from sleep mode to listen for paging block  414 . Again, using the midamble of the burst, user equipment  100  determines the timing error between the expected arrival of the midamble and the actual arrival of the midamble of the burst, labeled ê 2 . Time tracking logic  122  uses timing error ê 2  and gain factor α 1  to determine the loop filter output c 2 . Time tracking logic  122  updates the differential adjustment factor, d 2 , adds the currently calculated loop filter output c 2  and the prior differential adjustment factor, d 1 . Note that time tracking logic  122  adds c 2  and d 1  because user equipment  100  is currently listening to the network with network identification two (i.e., SIM 2  network  132 ). Time tracking logic  122  determines the timing adjustment, δ 2 , for the next scheduled paging block using the loop filter output c 2  and subtracts the differential adjustment factor d 2 . Note that time tracking logic  122  subtracts d 2  because the currently received paging block  414  is from SIM 2  network  132  while the next scheduled paging block  404  is from SIM 1  network  130 . User equipment  100  may use timing adjustment, δ 2 , as the compensation factor to apply to internal time base  140  for predicting the expected arrival of the next paging block  404 . After user equipment  100  receives and processes paging block  414 , it may enter a sleep mode until the next paging block is scheduled to arrive. While in sleep mode, user equipment  100  may use its internal time base  140  along with timing adjustment, δ 2 , to predict the expected arrival of the next paging block  404 . 
     When user equipment  100  expects the next scheduled paging block  404 , user equipment wakes up from sleep mode to listen for paging block  404 . Again, using the midamble of the burst, user equipment  100  determines the timing error between the expected arrival of the midamble and the actual arrival of the midamble of the burst, labeled ê 3 . Time tracking logic  122  uses timing error ê 3  and gain factor α 1  to determine the loop filter output c 3 . Time tracking logic  122  updates the differential adjustment factor, d 3 , subtracting the currently calculated loop filter output c 3  from the prior differential adjustment factor, d 2 . Note that time tracking logic  122  subtracts c 3  from d 2  because user equipment  100  is currently listening to the network with network identification one (i.e., SIM 1  network  130 ). Time tracking logic  122  determines the timing adjustment, δ 3 , for the next scheduled paging block using the loop filter output c 3 . Note that time tracking logic  122  does not add or subtract d 3  because the currently received paging block  404  is from SIM 1  network  130  and the next scheduled paging block  406  is also from SIM 1  network  130 . User equipment  100  may use timing adjustment, δ 3 , as the compensation factor to apply to internal time base  140  for predicting the expected arrival of the next paging block  406 . After user equipment  100  receives and processes paging block  404 , it may enter a sleep mode until the next paging block is scheduled to arrive. While in sleep mode, user equipment  100  may use its internal time base  140  along with timing adjustment, δ 3 , to predict the expected arrival of the next paging block  406 . 
     When user equipment  100  expects the next scheduled paging block  406 , user equipment wakes up from sleep mode to listen for paging block  406 . Again, using the midamble of the burst, user equipment  100  determines the timing error between the expected arrival of the midamble and the actual arrival of the midamble of the burst, labeled ê 4 . Time tracking logic  122  uses timing error ê 4  and gain factor α 1  to determine the loop filter output c 4 . Time tracking logic  122  updates the differential adjustment factor, d 4 , subtracting the currently calculated loop filter output c 4  from the prior differential adjustment factor, d 3 . Note that time tracking logic  122  subtracts c 4  from d 3  because user equipment  100  is currently listening to the network with network identification one (i.e., SIM 1  network  130 ). Because the timing adjustment, δ 4 , for the next scheduled paging block depends on whether the next scheduled paging block will be received on the same network or whether the paging block with be received from another network, the time tracking logic  122  may not determine the timing adjustment for the next paging block until user equipment  100  determines whether the next scheduled paging block will arrive from SIM 1  network  130  or SIM 2  network  132 . 
     As shown through  FIGS. 6-8 , time tracking logic  122  may use paging blocks from either SIM 1  network  130  or SIM 2  network  132  to compensate for the phase timing error of the internal time base  140 , even if the paging blocks collide. In some implementations, the time tracking logic  122  may also compensate for the frequency timing error due to the frequency drift of the internal time base. The frequency timing error may be used in addition to the phase timing error to compensate the internal time base when user equipment  100  predicts the arrival of the next paging block. 
     In such an implementation, example time tracking parameters  128  may include: 
     
       
         
               
               
               
             
           
               
                 TABLE 3 
               
               
                   
               
               
                   
                 Parameter 
                   
               
               
                 Variable 
                 Type 
                 Description 
               
               
                   
               
             
             
               
                 α 1   
                 constant 
                 Gain of the first order phase locked loop. 
               
               
                   
                   
                 This constant may be used to stabilize the 
               
               
                   
                   
                 loop and may be set to a rational number 
               
               
                   
                   
                 less than one 
               
               
                 α d   
                 constant 
                 Gain of the “delta loop.” This constant 
               
               
                   
                   
                 may be used to stabilize the loop and may 
               
               
                   
                   
                 be set to a rational number less than one 
               
               
                 α p   
                 constant 
                 Gain of internal time base drift. This 
               
               
                   
                   
                 constant may be used to stabilize the 
               
               
                   
                   
                 updates to the internal time base drift 
               
               
                   
                   
                 and may be set to a rational number less 
               
               
                   
                   
                 than one 
               
               
                 L 
                 constant 
                 Length (in time) of the averaging window 
               
               
                   
                   
                 used in estimating the internal time base 
               
               
                   
                   
                 drift 
               
               
                 n 
                 index 
                 An index representing receipt of the current 
               
               
                   
                   
                 paging block; n + 1 is the next scheduled 
               
               
                   
                   
                 paging block 
               
               
                 i(n) 
                 input 
                 Network Identification (e.g., SIM1 network 
               
               
                   
                   
                 or SIM2 network) for the n-th paging block 
               
               
                 ê(n) 
                 input 
                 The measured timing error from the n-th 
               
               
                   
                   
                 paging block 
               
               
                 Δ s  (n) 
                 input 
                 Time since last paging block was received 
               
               
                 c 
                 internal state 
                 First order loop filter output 
               
               
                   
                 variable 
               
               
                 d 
                 internal state 
                 The differential adjustment applied when 
               
               
                   
                 variable 
                 the next scheduled paging block is from a 
               
               
                   
                   
                 different network 
               
               
                 {circumflex over (p)} s   
                 internal state 
                 Estimated drift rate of the internal time 
               
               
                   
                 variable 
                 base (in Hertz) 
               
               
                 δ 
                 internal 
                 Timing adjustment between the previous 
               
               
                   
                 variable 
                 paging block and the current paging block 
               
               
                 S Δ, i  i = 1, 2 
                 internal state 
                 Cumulative counts of the internal time 
               
               
                   
                 variable 
                 base 
               
               
                 S δ, i  i = 1, 2 
                 internal state 
                 Cumulative timing adjustments 
               
               
                   
                 variable 
               
               
                 q 
                 output 
                 Time base adjustment for the next paging 
               
               
                   
                   
                 block 
               
               
                   
               
             
          
         
       
     
     Using the time tracking parameters  128  listed above, the time tracking logic  122  may implement the following algorithm: 
     
       
         
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
             
               
             
           
               
                 TABLE 4 
               
               
                   
               
             
             
               
                 for n = 1,2, ... 
               
             
          
           
               
                   
                 % calculate loop filter output (phase error timing adjustment) 
               
               
                   
                 c = α 1 ê(n); 
               
               
                   
                 % update differential adjustment 
               
               
                   
                 d = d + (−1) i(n)  α d c; 
               
               
                   
                 % determine time base adjustment based on phase timing error 
               
             
          
           
               
                   
                 if 
                 i(n + 1) == i(n) 
                 then δ = c ; 
               
               
                   
                 elseif 
                 i(n + 1) == 1 
                 then δ = c − d; 
               
               
                   
                 elseif 
                 i(n + 1) == 2 
                 then δ = c + d; 
               
             
          
           
               
                   
                 end 
               
               
                   
                 % determine time base adjustment based on phase timing error 
               
               
                   
                 % and timing error due to frequency drift of the internal time base 
               
               
                   
                 q = δ + Δ s  (n) {circumflex over (p)} s   
               
               
                   
                 % update frequency timing offset parameters 
               
               
                   
                 S Δ,1  = S Δ,1  + Δ s  (n) ; 
               
               
                   
                 S Δ,2  = S Δ,2  + Δ s  (n); 
               
               
                   
                 S δ,1  = S δ,1  + δ; 
               
               
                   
                 S δ,2  = S δ,2  + δ; 
               
             
          
           
               
                   
                 if 
                 S Δ,i(n)  &gt; L 
                 then 
               
             
          
           
               
                   
                 % estimate internal time base frequency drift 
               
               
                   
                 {circumflex over (p)} s  = {circumflex over (p)} s  + α p S δ,i(n)  (n)/L ; 
               
               
                   
                 S Δ,i(n)  = 0 ; 
               
               
                   
                 S δ,i  = 0; 
               
             
          
           
               
                   
                 end 
               
             
          
           
               
                 end 
               
               
                   
               
             
          
         
       
     
     In one implementation using the above parameters and algorithm, time tracking logic  122 , in addition to determining the time base adjustment due to phase timing error, time tracking logic  122  may include an adjustment due to the frequency drift of the internal time base. Time tracking logic  122  may estimate the time base adjustment due to the frequency drift of the internal time base by multiplying the estimated internal time base frequency drift, {circumflex over (p)} s , by the time elapsed since the last paging block was received, Δ s (n). The internal time base frequency drift, {circumflex over (p)} s , may be estimated over a series of paging blocks using an averaging window, L. Time tracking logic  122  accumulates the actual time elapsed, S Δ , between reception of paging blocks and accumulates the accumulated phase timing error, S δ . Each time the actual time elapsed, S Δ , exceeds the length of the averaging window, L, the time tracking logic  122  may update the estimated internal time base frequency drift, {circumflex over (p)} s . Time tracking logic  122  may update the estimated internal time base frequency drift, {circumflex over (p)} s , by the estimated frequency error, calculated by a gain constant, α p , multiplied by the accumulated phase timing error, S δ , divided by the length of the averaging window, L. In addition, the time tracking logic  122  may accumulate the actual time elapsed between reception of paging blocks and accumulate the accumulated phase timing error for each SIM independently. 
       FIGS. 8-10  are similar in aspects to  FIGS. 5-7 . As discussed above, the time tracking logic  122  may use paging blocks from either SIM 1  network  130  or SIM 2  network  132  to compensate for the phase timing error of the internal time base  140 , even if the paging blocks collide, and even if the paging blocks arrive from different SIM networks. For each reception of the paging block, time tracking logic  122  may calculate, ê, c, d, and δ in the same way as described above for  FIGS. 5-7 . However, rather than using δ as the compensation factor to apply to internal time base  140  for predicting the expected arrival of the next paging block, the time tracking logic  122  may use timing compensation q, as shown in  FIGS. 8-10 . Timing compensation q includes the compensation factor for the phase timing error and differential offset, δ, as described above, and an additional compensation factor for the timing error from the frequency drift Δ s (n) {circumflex over (p)} s  of the internal time base. 
       FIG. 11  shows flow diagram  1100  and is one implementation of the time tracking logic  122 . User equipment  100  receives a paging block on SIM 1  network  130  or SIM 2  network  132  ( 1102 ) and processes the paging block to determine the timing error, ê(n), between the expected arrival of the paging block and the actual arrival of the paging block ( 1104 ). Next, time tracking logic  122  determines whether the current network is SIM 1  network  130  or SIM 2  network  132  ( 1106 ). If the current network is SIM 1  network  130 , timing differential, d, is updated by subtracting the loop output, c=α 1 ê(n), from the prior timing differential ( 1108 ). If the current network is SIM 2  network  132 , timing differential, d, is updated by adding the loop output, c=α 1 ê(n), and the prior timing differential ( 1110 ). 
     Next, the time tracking logic  122  determines which SIM network will receive the next paging block ( 1112 ). At block  1114 , if the next paging block is on the same network, the timing offset is determined using option  1  ( 1118 ). If the time tracking logic  122  uses option  1 , the timing offset is set to the phase timing error from the loop output, δ=c=α 1 ê(n), and does not account for the timing differential, d. On the other hand if, at block  1116 , the next paging block switches from SIM 2  to SIM 1 , then the timing offset is determined using option  2  ( 1120 ). If the time tracking logic  122  uses option  2 , the timing offset is set to the phase timing error from the loop output and subtracts the timing differential, d, between SIM 2  and SIM 1 . Thus, δ=c−α d d. On the other hand if, at block  1116 , the next paging block switches from SIM 1  to SIM 2 , then the timing offset is determined using option  3  ( 1122 ). If the time tracking logic  122  uses option  3 , the timing offset is set to the phase timing error from the loop output and adds the timing differential, d, between SIM 1  and SIM 2 . Thus, δ=c+α d d. 
     Next, the time tracking logic  122  determines the time base adjustment, q, which takes into account the phase timing error, the timing differential, and the frequency timing offset ( 1124 ). q=δ+Δ s (n){circumflex over (p)} s . User equipment  100  may use q as the compensation factor for adjusting the internal time base  140  when predicting the timing of the next scheduled paging block. Next, time tracking logic  122  accumulates the actual time elapsed, S Δ , between reception of paging blocks and accumulates the accumulated phase timing error, S δ  ( 1126 ). At block  1128 , time tracking logic  122  determines whether the actual time elapsed, S Δ , exceeds the length of the averaging window, L. If the actual time elapsed, S Δ , exceeds the length of the averaging window, L, the time tracking logic  122  may update the estimated internal time base frequency drift, {circumflex over (p)} s  ( 1130 ). In block  1132 , the time tracking logic  122  determines whether to continue listening for the next paging block. 
     The methods, devices, techniques, and logic described above may be implemented in many different ways in many different combinations of hardware, software or both hardware and software. For example, all or parts of the system may include circuitry in a controller, a microprocessor, or an application specific integrated circuit (ASIC), or may be implemented with discrete logic or components, or a combination of other types of analog or digital circuitry, combined on a single integrated circuit or distributed among multiple integrated circuits. All or part of the logic described above may be implemented as instructions for execution by a processor, controller, or other processing device and may be stored in a tangible or non-transitory machine-readable or computer-readable medium such as flash memory, random access memory (RAM) or read only memory (ROM), erasable programmable read only memory (EPROM) or other machine-readable medium such as a compact disc read only memory (CDROM), or magnetic or optical disk. Thus, a product, such as a computer program product, may include a storage medium and computer readable instructions stored on the medium, which when executed in an endpoint, computer system, or other device, cause the device to perform operations according to any of the description above. 
     The processing capability of the system may be distributed among multiple system components, such as among multiple processors and memories, optionally including multiple distributed processing systems. Parameters, databases, and other data structures may be separately stored and managed, may be incorporated into a single memory or database, may be logically and physically organized in many different ways, and may implemented in many ways, including data structures such as linked lists, hash tables, or implicit storage mechanisms. Programs may be parts (e.g., subroutines) of a single program, separate programs, distributed across several memories and processors, or implemented in many different ways, such as in a library, such as a shared library (e.g., a dynamic link library (DLL)). The DLL, for example, may store code that performs any of the system processing described above. While various embodiments of the invention have been described, it will be apparent to those of ordinary skill in the art that many more embodiments and implementations are possible within the scope of the invention. Accordingly, the invention is not to be restricted except in light of the attached claims and their equivalents.