# Patent

## Title
Techniques to control uplink power

## Abstract

Techniques are described that provide uplink power control techniques that can support different uplink multi-input multi-output (MIMO) transmission schemes. Open and closed loop power control schemes can be used to prescribe the power level of the mobile station.

## Background
This application is a divisional of U.S. patent application Ser. No. 12/590,546, filed on Nov. 10, 2009, now issued as U.S. Pat. No. 8,340,593, which is incorporated herein by reference in its entirety.


FIELD
The subject matter disclosed herein relates generally to techniques to determine transmitter power of a wireless signal.
RELATED ART
In wireless networks, OFDM/OFDMA with multi-input multi-output (MIMO) is an important technology for next-generation mobile broadband networks. Uplink power control is an extremely important component of MIMO OFDM/OFDMA. Uplink power control involves controlling the transmit power level to balance the link performance and terminal battery power and to reduce the inter-base station uplink co-channel interference. Increasing transmission power of one mobile station enjoys the increase of its link performance but increases interferences to other mobile stations of neighboring base stations because they use the same channel. This results in decreased link performance of the other mobile stations. Therefore, in deciding uplink power level, it is important to balance the performance of a particular link with interference to the other base stations.
Current power control schemes focus on the uplink power control for a single transmit antenna at the mobile station without considering uplink MIMO operation. Uplink MIMO operation can be implemented as single-user MIMO (SU-MIMO) by using more than one transmit antenna at the mobile station. Uplink MIMO operation can also be implemented as a MU-MIMO (also known as collaborative MIMO) by allowing simultaneous uplink transmission from two or more mobile stations in the same frequency and time resource, where each mobile station can use one or more transmit antennas.



BRIEF DESCRIPTION OF THE DRAWINGS
Embodiments of the present invention are illustrated by way of example, and not by way of limitation, in the drawings and in which like reference numerals refer to similar elements.
FIG. 1 depicts in block diagram form, an information exchange between a base station and mobile station during an open loop power control (OLPC) mode, in accordance with an embodiment.
FIG. 2 depicts in block diagram form, an information exchange between a base station and mobile station during a closed loop power control (CLPC) mode, in accordance with an embodiment.
FIG. 3 depicts an example process that can be used by a mobile station to determine transmitter power using open loop power control (OLPC) mode, in accordance with an embodiment.
FIG. 4 depicts an example process that can be used by a mobile station to determine transmitter power using closed loop power control (CLPC), in accordance with an embodiment.
FIG. 5 depicts an example of a virtual cell model, in accordance with an embodiment.
FIG. 6 depicts a cumulative density function (CDF) of user throughput.
FIG. 7A depicts a performance curve for some simulation results.
FIG. 7B depicts an interference over thermal control curve for some simulation results.



DETAILED DESCRIPTION
Reference throughout this specification to “one embodiment” or “an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, the appearances of the phrase “in one embodiment” or “an embodiment” in various places throughout this specification are not necessarily all referring to the same embodiment. Furthermore, the particular features, structures, or characteristics may be combined in one or more embodiments.
Embodiments of the invention may be used in a variety of applications. Some embodiments of the invention may be used in conjunction with various devices and systems, for example, a transmitter, a receiver, a transceiver, a transmitter-receiver, a wireless communication station, a wireless communication device, a wireless Access Point (AP), a modem, a wireless modem, a Personal Computer (PC), a desktop computer, a mobile computer, a laptop computer, a notebook computer, a tablet computer, a server computer, a handheld computer, a handheld device, a Personal Digital Assistant (PDA) device, a handheld PDA device, a network, a wireless network, a Local Area Network (LAN), a Wireless LAN (WLAN), a Metropolitan Area Network (MAN), a Wireless MAN (WMAN), a Wide Area Network (WAN), a Wireless WAN (WWAN), devices and/or networks operating in accordance with existing IEEE 802.11, 802.11a, 802.11b, 802.11e, 802.11g, 802.11h, 802.11i, 802.11n, 802.16, 802.16d, 802.16e, 802.16m, or 3GPP standards and/or future versions and/or derivatives and/or Long Term Evolution (LTE) of the above standards, a Personal Area Network (PAN), a Wireless PAN (WPAN), units and/or devices which are part of the above WLAN and/or PAN and/or WPAN networks, one way and/or two-way radio communication systems, cellular radio-telephone communication systems, a cellular telephone, a wireless telephone, a Personal Communication Systems (PCS) device, a PDA device which incorporates a wireless communication device, a Multiple Input Multiple Output (MIMO) transceiver or device, a Single Input Multiple Output (SIMO) transceiver or device, a Multiple Input Single Output (MISO) transceiver or device, a Multi Receiver Chain (MRC) transceiver or device, a transceiver or device having “smart antenna” technology or multiple antenna technology, or the like. Some embodiments of the invention may be used in conjunction with one or more types of wireless communication signals and/or systems, for example, Radio Frequency (RF), Infra Red (IR), Frequency-Division Multiplexing (FDM), Orthogonal FDM (OFDM), Orthogonal Frequency Division Multiple Access (OFDMA), Time-Division Multiplexing (TDM), Time-Division Multiple Access (TDMA), Extended TDMA (E-TDMA), General Packet Radio Service (GPRS), Extended GPRS, Code-Division Multiple Access (CDMA), Wideband CDMA (WCDMA), CDMA 2000, Multi-Carrier Modulation (MDM), Discrete Multi-Tone (DMT), Bluetooth®, ZigBeeTM, or the like. Embodiments of the invention may be used in various other apparatuses, devices, systems and/or networks. IEEE 802.11x may refer to any existing IEEE 802.11 specification, including but not limited to IEEE 802.11a, 802.11b, 802.11e, 802.11g, 802.11h, 802.11i, and 802.11n as well as any version or draft of IEEE 802.16e and IEEE 802.16m.
Some embodiments provide uplink power control (ULPC) techniques that can support different uplink multi-input multi-output (MIMO) transmission schemes for both open and closed loop power control. Some embodiments provide ULPC techniques based on the rule of maximum uplink spectral efficiency (SE). Some embodiments support the operation of different mobile stations using different uplink multi-input multi-output (MIMO) transmission schemes and different transmit (Tx) antennas. Embodiments can be applied to next generation OFDMA-based wireless broadband technologies and related products, such as, but not limited to, IEEE 802.16e, IEEE 802.16m, 3GPP LTE, as well as 3GPP2 UMB, to increase the uplink spectral efficiency significantly by controlling the uplink interference and the tradeoff between the uplink cell-edge user spectral efficiency and the uplink average spectral efficiency.
In various embodiments, for MU-SIMO, the following target signal to interference and noise ratio can be applied:

SINRTarget=γ×SIRDL−β

Variable γ is used to control interference. If neighbor sectors have higher percentage of MU-MIMO selection, γ can be decreased to reduce interference in the network and maximize the overall spectral efficiency. β is the offset value to achieve the maximum spectral efficiency, and it can be applied as:





  
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where Nr is the number of receive antennas at the base station. However, β can be other values. In various embodiments, when the mobile station switches between the SU-MIMO and MU-MIMO, the same Tx power can be used.

Various embodiments can control the interference in the network, provide a good tradeoff between the overall system spectral efficiency and cell-edge user performance, and support different uplink SU-MIMO and MU-MIMO cases with the same control scheme.
FIG. 1 depicts in block diagram form, an information exchange between a base station and a mobile station during an open loop power control (OLPC) mode, in accordance with an embodiment. Base station 102 can receive information such as noise and interference level (NI) from neighboring base stations (not shown) using a network (not depicted) such as but not limited to a backhaul network. Base station 102 can broadcast or unicast to mobile station 104 a control factor γ, SINRMIN, as well as the NI information of the frequency partition that the mobile station is assigned. Control factor γ represents a fairness and interference over thermal (IoT) control factor. Control factor γ can be determined by the base station using a vendor-specific methodology. For example, if neighbor sectors have higher percentage of MU-MIMO selection, control factor γ can be decreased to reduce interference in the network and maximize the overall spectral efficiency. For example, when the base station is informed that the neighboring base stations have high uplink interference level, control factor γ can be reduced. Otherwise, the same level is maintained or can be increased.
SINRMIN represents the signal to interference and noise ratio (SINR) requirement for the minimum data rate expected by the base station and is described with regard to equation (b) below.
Base station 102 can decide to broadcast or unicast control factor γ, SINRMIN, and NI to mobile station 104 in a manner defined in the IEEE 802.16m Draft Standard (D1) (2009). A decision to broadcast or unicast may be made by base station 102 using any vendor specific technique. Base station 102 can decide the broadcast or unicast period.
After mobile station 104 receives γ, SINRMIN, and NI from base station 102, mobile station 104 can use the OLPC transmission power control calculation formula in equation (a) to determine its transmission power per subcarrier and per antenna:

P(dBm)=L+SINRTarget+NI  (a)

where:

    
    
        P is the TX power level (dBm) per subcarrier from each transmit (Tx) antenna. The mobile station's Tx antenna gain may be factored into determination of P. For IEEE 802.16m Draft Standard (D1) (2009) compliant mobile stations, power level P is determined for each stream.
        L is the estimated average current uplink propagation loss, which considers the mobile station's Tx antenna gain and path loss but may exclude the base station's Rx antenna gain. L may be determined by a mobile station from downlink signaling. Due to channel reciprocity, the measured downlink average path loss is used to estimate the uplink average path loss.
        SINRTarget is calculated based on equation (b) below.
        NI is the estimated average power level (dBm) of the noise and interference per subcarrier at the base station and may not consider the base station's Rx antenna gain. Techniques for determining noise plus interference level are well known and described, for example, in sections 8.3.7.4.2, 8.4.10.3.2, 8.4.11.3, 8.4.5.3.19, and 8.3.9.3 of IEEE 802.16 Rev2/D7 (October 2008).
    
    


Various embodiments implement the signal to interference and noise ratio (SINR) target of the IEEE 802.16e and IEEE 802.16m standards using of the following equation:




  
    
      
        
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where

    
    
        SINRMIN is the SINR requirement for the minimum data rate expected by the base station. In various embodiments, SINRMIN is determined by the base station using vendor-specific techniques.
        Nr is the number of receive antennas at the base station.
        SINRDL is the ratio of useful downlink signal to the downlink interference power measured at the mobile station. SINRDL can be selected by a base station using a vendor-specific technique.
    
    


Various embodiments support multi-mode operation for IEEE 802.16m network communications and legacy IEEE 802.16e communications. When open-loop power control is used to control transmission power of a mobile station, the power per subcarrier and per transmit (Tx) antenna for the uplink transmission for uplink bursts can be set according to equation (c):

P(dBm)=L+SINRTarget+NI+Offset_AMSperAMS+Offset_ABSperAMS  (c)

where

    
    
        P is the TX power level (dBm) per subcarrier and for a single transmission antenna for the current transmission. For IEEE 802.16m Draft Standard (D1) (2009) compliant systems, P is the power output per stream.
        L is the estimated average current uplink propagation loss and includes AMS's Tx antenna gain and path loss. AMS refers to an Advanced Mobile Station as described in IEEE 802.16m Draft Standard (D1) (2009), although L can be determined for any mobile station in a manner described in the IEEE 802.16e standard. L may be determined based on the total power received on the active subcarriers of the frame preamble and with reference to the BS_EIRP parameter sent by the advanced base station. For open loop power control, L may be determined by the mobile station. For example, L may be determined by the mobile station for open link power control by measuring total downlink power received from a preamble and by using the BS_EIRP parameter sent by a base station. For example, L can be estimated by channel symmetry: L=BS_EIRP−RSS, where RSS is Received Signal Strength of received preamble.
        SINRTarget is the target uplink SINR received by an advanced base station (ABS) and is described with regard to equation (d) below. ABS is described for example in the IEEE 802.16m Draft Standard (D1) (2009). However, the target uplink SINR can be that received by IEEE 802.16e base stations.
        NI is the estimated average power level (dBm) of the noise and interference per subcarrier at the ABS, not including ABS's Rx antenna gain.
        Offset_AMSperAMS is a correction term for AMS-specific power offset. This value may be controlled by the AMS and its initial value may be set to zero. In IEEE 802.16m Draft Standard (D1) (2009), determination of the Offset_AMSperAMS value is described with regard to “Offset_SSperSS,” as well as Section 8.4.10.3.2, “passive UL open-loop power control,” and “active UL open-loop power control.”
        Offset_ABSperAMS is also a correction term for AMS-specific power offset. This value may be controlled by an ABS using power control messages. Determination of Offset_ABSperAMS is made by an ABS. The ABS has the flexibility to decide Offset_ABSperAMS using a vendor specific technique.
    
    


When the mobile station connects to a network, mobile station 104 can negotiate which SINRTarget calculation formula to support. The selected SINRTarget calculation formula may be signaled using a power control message. In various embodiments, two modes can be selected. For modes 1 and 2, the SINRTarget is defined as:




  
    
      
        
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        R is the number of repetitions for the modulation/FEC rate. Determination of C/N may be described with regard to table 514 in section 8.4.10.3 of IEEE 802.16-2009.
        SINROPT is the target SINR value for IoT control and provides a tradeoff between overall system throughput and cell edge performance. SINROPT can be determined using the following equation:
    
    






  
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where

    
    
        SINRMIN is the SINR requirement for the minimum rate expected by the ABS and can be set using a power control message. In various embodiments, SINRMIN is a 4 bit field and represents the dB value among {−3, −2.5, −2, −1.5, −1, 0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5}. Selection of SINRMIN can be made using a vendor-specific technique.
        γ represents the fairness and IoT control factor and may be decided by the ABS and set using a power control message. In various embodiments, γ is a 4 bit field and represents a value among {0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2, 1.3, 1.4, 1.5}. Selection of γ can be made using a vendor-specific technique.
        SINRDL represents the ratio of downlink signal to interference and noise power, as measured by the AMS. Determination of SINRDL can be made using a technique to determine CINR that is described in section 8.4.11.1 of IEEE 802.16-2009.
        Nr represents the number of receive antennas at the ABS.
    
    


FIG. 2 depicts in block diagram form, an information exchange between a base station and mobile station during a closed loop power control mode, in accordance with an embodiment. Base station 202 may not broadcast the γ, SINRMIN, and NI to mobile station 204. Instead, mobile station 204 reports the ratio of downlink useful signal to the downlink interference power measured at mobile station 204 (SIRDL) to base station 202 so that base station 202 can determine the uplink transmission power of mobile station 204. In various embodiments, mobile station 204 is to measure the SIRDL based on the downlink preamble signal strength and report the SIRDL to base station 202. After base station 202 receives the path loss information from mobile station 204, base station 202 is to determine uplink power level of mobile station 204 using the following procedure.
(1) Measure the path loss based on the mobile station's previous transmission(s) of SIRDL to the base station. Determination of path loss from SIRDL can be made by the base station based on the received signal power of message and AMS Tx power. For example, path loss can be determined using the following formula: P_dB(AMS Tx Power)−P_dB(received power). By contrast, determination of estimated average current uplink propagation loss (L) is made by using the measurement of a downlink pathloss value.
(2) Based on SIRDL and the path loss information, calculate the transmission power of the mobile station according to equation (a) or (c). Path loss information is substituted for the L value in equations (a) and (c).
(3) Unicast the power level to mobile station 204. In various embodiments, messages described with regard to section 8.4.11.1 of IEEE 802.16-2009 can be used to transmit SIRDL and power level.
FIG. 3 depicts an example process that can be used by a mobile station to determine transmitter power using open loop power control (OLPC) mode, in accordance with an embodiment.
Block 302 includes neighboring base stations exchanging information such as noise and interference level. In various embodiments, a wireless service operator decides what base stations are neighboring based in part on a layout and locations of base stations. For example, a network such as a backhaul network can be used to exchange information.
Block 304 includes a base station transmitting a control factor γ and SINRMIN to the mobile station as well as the noise and interference of the frequency partition that the mobile station is assigned. For example, the base station may transmit control factor γ, SINRMIN, and noise and interference by broadcasting or unicasting. The base station can decide the broadcast or unicast period. The base station can determine the control factor γ and SINRMIN using vendor-specific techniques.
Block 306 includes the mobile station determining a transmit power level. For example, techniques to determine transmit power level are described with regard to equations (a) or (c).
Block 308 includes the mobile station transmitting the uplink signal to the base station at the determined transmit power level.
FIG. 4 depicts an example process that can be used by a mobile station to determine transmitter power using closed loop power control (CLPC), in accordance with an embodiment.
Block 402 includes the mobile station measuring the SIRDL based on the downlink preamble signal strength and reporting the SIRDL to the base station associated with the mobile station.
Block 404 includes the base station measuring the path loss based on the mobile station's previous transmission(s) of SIRDL. Determination of path loss from SIRDL can be made by the base station based on the received signal power message and AMS Tx power.
Block 406 includes the base station determining the transmission power of the mobile station according to equation (a) or (c) based on SIRDL and the path loss information. Path loss information is substituted for the L value in equations (a) and (c).
Block 408 includes the base station transmitting the power level to the mobile station. Thereafter, the mobile station can transmit at the prescribed power level.
Various embodiments include increasing the Tx PSD by step ΔPSD and determining a Tx power spectral density, PSDTX, until the spectral efficiency (SE) change is negative. For example, SE change can be defined as the difference of the SE gain in the home (or serving) sector and the SE loss in the neighboring sectors.
To predict the SE loss in the i-th neighboring sector, the following information may be first obtained: (a) channel loss CLi from the mobile station to the i-th neighboring base station, (b) noise plus Interference level NI, in the i-th neighboring sector, and (c) transmit power density PSDTX,i of the mobile station operating on the same channel in the i-th neighboring sector.
When a mobile station enters a network, the channel loss CLH and CLi from the mobile station to the home base station and the ith neighboring base station (i=1, 2, . . . , N) can be estimated by using the downlink preamble (synchronization channel). Among these parameters, CLi can be estimated at the mobile station using the downlink preamble sent from the i-th base station, and NIi must be first exchanged among the base stations and then broadcast. However, obtaining such information is at the cost of high feedback overhead and complicated hardware realization.
Noise plus Interference level (NI) is the sum of the power density of noise and interference which can be estimated at each base station. Neighboring NI (NI1, NI2, . . . , NIN) can be acquired by exchanging information among the base stations through the network backhaul or other manners. The home NI (NIH) can be broadcast by the base station. The relationship between NI and IoT can be expressed as:

NI=IoT*PNoise+PNoise 

where PNoise is the thermal noise power density.
A virtual cell model can be used to predict the SE loss in all neighboring sectors. FIG. 5 depicts an example of a virtual cell model, in accordance with an embodiment. Assume that there exists a virtual neighboring base station which suffers from the combined interference caused by the current mobile station to the neighboring sectors 1 ̃N. The channel loss from mobile station to this virtual base station is defined as CLi. Then, the following equation holds:




  
    
      
        
          
            
              
                
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Using this equivalent channel loss allows estimation of the SINR of the downlink preamble for uplink power control but not each individual CLi.

In general, each cell can use single-user MIMO (SU-MIMO) or MU-MIMO. Accordingly, the minimum SINR (SINRMIN) are determined for four combinations: (1) home cell SU-MIMO and virtual cell SU-MIMO, (2) home cell MU-MIMO and virtual cell SU-MIMO, (3) home cell SU-MIMO and virtual cell MU-MIMO, and (4) home cell MU-MIMO and virtual cell MU-MIMO. It can be shown that the power control formula based on the above idea can be unified into the signal to interference and noise ratio (SINR) of equation (b).
In the case of home cell SU-MIMO and virtual cell SU-MIMO, the SE gain in the home sector for each mobile station can be modeled in the following manner. Suppose that the current power spectral density is PSDTX,Ant and the Tx power density increases by a small step, ΔPSD. Then, the new power density is PSDNew,Ant=PSDTX,Ant++ΔPSD and the resulting SE improvement is




  
    
      
        
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                  S
                  ⁢
                  
                    
                  
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                        ⁢
                        
                          
                        
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                        t
                      
                    
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              )
            
          
          -
          
            log
            ⁡
            
              (
              
                1
                +
                
                  
                    N
                    r
                  
                  *
                  S
                  ⁢
                  
                    
                  
                  ⁢
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                  ⁢
                  
                    
                  
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              )
            
          
        
      
    
  
  
    
      
        =
        
        ⁢
        
          log
          (
          
            
              1
              +
              
                
                  N
                  r
                
                *
                S
                ⁢
                
                  
                
                ⁢
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                ⁢
                
                  
                
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              +
              
                
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                *
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                ⁢
                
                  
                
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                ⁢
                
                  
                
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                      n
                      ⁢
                      
                        
                      
                      ⁢
                      t
                    
                  
                  H
                
              
            
          
          )
        
      
    
  




where,

    
    
        SINR is the Signal to Interference plus Noise Ratio,
        SINRNew,AntH is the new SINR per receive antenna after increasing the power spectral density by ΔPSD,
        SINROrig,AntH is the original SINR per receive antenna and
        Nr is the number of receive antenna.
    
    


In general, the instantaneous channel realization is estimated in advance so as to compute the exact SINR. However, this requires large computational overhead and results in long processing delay. Using the slow fading estimation to compute the SINR, and the resulting SE gain is meaningful in the sense of stochastic average. Based on those assumptions, the following computations are made:



  
    
      S
      ⁢
      
        
      
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      I
      ⁢
      
        
      
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      ⁢
      
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            t
          
        
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    =
    
      
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              ⁢
              
                
              
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            ,
            
              A
              ⁢
              
                
              
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              ⁢
              
                
              
              ⁢
              t
            
          
        
        ⁢
        
          /
        
        ⁢
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          H
        
      
      
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        ⁢
        
          
        
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              ⁢
              
                
              
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              n
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              t
            
          
        
      
    
  




  
    
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    =
    
      
        
          (
          
            
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            +
            
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              ⁢
              
                
              
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              ⁢
              
                
              
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          )
        
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              ⁢
              
                
              
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              t
            
          
        
      
    
  



The SE gain after increasing the power spectral density of this mobile station becomes:





  
    
      
        
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          ⁢
          
            
          
          ⁢
          
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              ⁢
              
                
              
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        =
        
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          (
          
            
              1
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                    (
                    
                      
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                    )
                  
                
                
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The SE loss in the virtual sector can be expressed as




  
    
      
        
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          log
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        =
        
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          (
          
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                          ⁢
                          
                            
                          
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                          ⁢
                          
                            
                          
                          ⁢
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                  +
                  
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                    ⁢
                    
                      
                    
                    ⁢
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                    ⁢
                    
                      
                    
                    ⁢
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                    ⁢
                    
                      
                    
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                    ⁢
                    
                      /
                    
                    ⁢
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                    ⁢
                    
                      
                    
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                      L
                      I
                    
                  
                
              
            
          
          )
        
      
    
  




As already mentioned, the SE change is defined as the improvement of the SE gain in the home sector over the SE loss in all the neighboring sectors, which can be approximated as SELossI. If increasing the Tx power spectral density leads to a positive SE change, then the overall throughput in all sectors should increase as well, as well as seeking higher Tx power spectral density. On the contrary, if a negative SE change is calculated, then increasing the Tx power spectral density is not beneficial, and the original power density should be the best level obtainable. From this perspective, the best Tx power spectral density is the level such that the SE change equals to 0 when ΔPSD→0 and leads to signal to interference and noise ratio of equation (b):



  
    
      Δ
      ⁢
      
        
      
      ⁢
      S
      ⁢
      
        
      
      ⁢
      E
    
    =
    
    ⁢
    
      
        
          S
          ⁢
          
            
          
          ⁢
          
            E
            
              G
              ⁢
              
                
              
              ⁢
              a
              ⁢
              
                
              
              ⁢
              i
              ⁢
              
                
              
              ⁢
              n
            
          
        
        -
        
          S
          ⁢
          
            
          
          ⁢
          
            E
            
              L
              ⁢
              
                
              
              ⁢
              o
              ⁢
              
                
              
              ⁢
              s
              ⁢
              
                
              
              ⁢
              s
            
            I
          
        
      
      =
      
        
          
            0
            ⁢
            
              (
              
                
                  Δ
                  ⁢
                  
                    
                  
                  ⁢
                  P
                  ⁢
                  
                    
                  
                  ⁢
                  S
                  ⁢
                  
                    
                  
                  ⁢
                  D
                
                →
                0
              
              )
            
          
          ⁢
          
            

          
          ⇒
          
            
              
                
                  N
                  r
                
                *
                Δ
                ⁢
                
                  
                
                ⁢
                P
                ⁢
                
                  
                
                ⁢
                S
                ⁢
                
                  
                
                ⁢
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                ⁢
                
                  
                
                ⁢
                
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                ⁢
                
                  
                
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                      t
                    
                  
                
              
              +
              
                
                  
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                  ⁢
                  
                    
                  
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        =
        
          
            
              
                
                  
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                  +
                  
                    
                      
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To guarantee the throughput of cell-edge users, it is always beneficial to limit the minimum SINR (SINRMIN), which leads to signal to interference and noise ratio of equation (b).
In the case of home cell MU and virtual cell SU, the SE gain corresponds to gain from two users and can be expressed as:




  
    
      
        
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          )
        
      
    
  




Because MU-MIMO is used in the home cell, the interference power to the virtual cell is also doubled:




  
    
      
        
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Then, the derived optimal Tx power spectral density leads to signal to interference and noise ratio of equation (b).



  
    
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            ⇒
            
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                γ
              
              *
              
                
                  
                    
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          =
          
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            -
            
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In the case of home cell SU and virtual cell MU, the SE gain is the same as derived for home cell SU-MIMO and virtual cell SU-MIMO. However, the SE loss should be doubled, i.e.,




  
    
      
        
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          ⁢
          
            
          
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        =
        
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          *
          
            log
            (
            
              
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                          t
                        
                      
                    
                    *
                    
                      P
                      
                        
                          N
                          ⁢
                          
                            
                          
                          ⁢
                          o
                          ⁢
                          
                            
                          
                          ⁢
                          i
                          ⁢
                          
                            
                          
                          ⁢
                          s
                          ⁢
                          
                            
                          
                          ⁢
                          e
                        
                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                  
                  
                    N
                    ⁢
                    
                      
                    
                    ⁢
                    
                      I
                      
                        I
                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                  
                
              
              
                1
                +
                
                  
                    
                      N
                      r
                    
                    *
                    S
                    ⁢
                    
                      
                    
                    ⁢
                    N
                    ⁢
                    
                      
                    
                    ⁢
                    
                      R
                      
                        I
                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                    *
                    
                      P
                      
                        
                          N
                          ⁢
                          
                            
                          
                          ⁢
                          o
                          ⁢
                          
                            
                          
                          ⁢
                          i
                          ⁢
                          
                            
                          
                          ⁢
                          s
                          ⁢
                          
                            
                          
                          ⁢
                          e
                        
                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                  
                  
                    
                      N
                      ⁢
                      
                        
                      
                      ⁢
                      
                        I
                        
                          I
                          ,
                          
                            A
                            ⁢
                            
                              
                            
                            ⁢
                            n
                            ⁢
                            
                              
                            
                            ⁢
                            t
                          
                        
                      
                    
                    +
                    
                      Δ
                      ⁢
                      
                        
                      
                      ⁢
                      P
                      ⁢
                      
                        
                      
                      ⁢
                      S
                      ⁢
                      
                        
                      
                      ⁢
                      D
                      ⁢
                      
                        /
                      
                      ⁢
                      C
                      ⁢
                      
                        
                      
                      ⁢
                      
                        L
                        I
                      
                    
                  
                
              
            
            )
          
        
      
    
  
  
    
      
        =
        
        ⁢
        
          
            log
            (
            
              
                1
                +
                
                  
                    
                      N
                      r
                    
                    *
                    S
                    ⁢
                    
                      
                    
                    ⁢
                    N
                    ⁢
                    
                      
                    
                    ⁢
                    
                      R
                      
                        I
                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                    *
                    
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                          N
                          ⁢
                          
                            
                          
                          ⁢
                          o
                          ⁢
                          
                            
                          
                          ⁢
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                          ⁢
                          
                            
                          
                          ⁢
                          s
                          ⁢
                          
                            
                          
                          ⁢
                          e
                        
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                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
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                    ⁢
                    
                      
                    
                    ⁢
                    
                      I
                      
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                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                  
                
              
              
                1
                +
                
                  
                    
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                    *
                    S
                    ⁢
                    
                      
                    
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                    ⁢
                    
                      
                    
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                        ,
                        
                          A
                          ⁢
                          
                            
                          
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                          n
                          ⁢
                          
                            
                          
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                          ⁢
                          
                            
                          
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                          ⁢
                          
                            
                          
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                          ⁢
                          
                            
                          
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                      ⁢
                      
                        
                      
                      ⁢
                      
                        I
                        
                          I
                          ,
                          
                            A
                            ⁢
                            
                              
                            
                            ⁢
                            n
                            ⁢
                            
                              
                            
                            ⁢
                            t
                          
                        
                      
                    
                    +
                    
                      Δ
                      ⁢
                      
                        
                      
                      ⁢
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                      ⁢
                      
                        
                      
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                      ⁢
                      
                        
                      
                      ⁢
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                      ⁢
                      
                        /
                      
                      ⁢
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                      ⁢
                      
                        
                      
                      ⁢
                      
                        L
                        I
                      
                    
                  
                
              
            
            )
          
          2
        
      
    
  
  
    
      
        ≈
        
        ⁢
        
          log
          (
          
            1
            +
            
              
                
                  
                    2
                    *
                    Δ
                    ⁢
                    
                      
                    
                    ⁢
                    P
                    ⁢
                    
                      
                    
                    ⁢
                    S
                    ⁢
                    
                      
                    
                    ⁢
                    D
                  
                  
                    C
                    ⁢
                    
                      
                    
                    ⁢
                    
                      
                        L
                        ⁢
                        
                          
                        
                      
                      I
                    
                    *
                    N
                    ⁢
                    
                      
                    
                    ⁢
                    
                      I
                      
                        I
                        ,
                        
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                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                  
                
                
                  1
                  +
                  
                    
                      
                        N
                        r
                      
                      *
                      S
                      ⁢
                      
                        
                      
                      ⁢
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                      ⁢
                      
                        
                      
                      ⁢
                      
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                            ⁢
                            
                              
                            
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                            n
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                              ⁢
                              
                                
                              
                              ⁢
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                      +
                      
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                        ⁢
                        
                          
                        
                        ⁢
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                        ⁢
                        
                          
                        
                        ⁢
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                        ⁢
                        
                          
                        
                        ⁢
                        D
                        ⁢
                        
                          /
                        
                        ⁢
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                        ⁢
                        
                          
                        
                        ⁢
                        
                          L
                          I
                        
                      
                    
                  
                
              
              ⁢
              
                
                  
                    N
                    r
                  
                  *
                  S
                  ⁢
                  
                    
                  
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                  N
                  ⁢
                  
                    
                  
                  ⁢
                  
                    R
                    
                      I
                      ,
                      
                        A
                        ⁢
                        
                          
                        
                        ⁢
                        n
                        ⁢
                        
                          
                        
                        ⁢
                        t
                      
                    
                  
                  *
                  
                    P
                    
                      
                        N
                        ⁢
                        
                          
                        
                        ⁢
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                        ⁢
                        
                          
                        
                        ⁢
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                        ⁢
                        
                          
                        
                        ⁢
                        s
                        ⁢
                        
                          
                        
                        ⁢
                        e
                      
                      ,
                      
                        A
                        ⁢
                        
                          
                        
                        ⁢
                        n
                        ⁢
                        
                          
                        
                        ⁢
                        t
                      
                    
                  
                
                
                  
                    N
                    ⁢
                    
                      
                    
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                        I
                        ,
                        
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                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                  
                  +
                  
                    Δ
                    ⁢
                    
                      
                    
                    ⁢
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                    ⁢
                    
                      
                    
                    ⁢
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                    ⁢
                    
                      
                    
                    ⁢
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                    ⁢
                    
                      /
                    
                    ⁢
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                    ⁢
                    
                      
                    
                    ⁢
                    
                      L
                      I
                    
                  
                
              
            
          
          )
        
      
    
  




In this case, the optimal Tx power spectral density leads to signal to interference and noise ratio of equation (b):



  
    
      Δ
      ⁢
      
        
      
      ⁢
      S
      ⁢
      
        
      
      ⁢
      E
    
    =
    
      
        
          S
          ⁢
          
            
          
          ⁢
          
            E
            
              G
              ⁢
              
                
              
              ⁢
              a
              ⁢
              
                
              
              ⁢
              i
              ⁢
              
                
              
              ⁢
              n
            
          
        
        -
        
          S
          ⁢
          
            
          
          ⁢
          
            E
            
              L
              ⁢
              
                
              
              ⁢
              o
              ⁢
              
                
              
              ⁢
              s
              ⁢
              
                
              
              ⁢
              s
            
            I
          
        
      
      =
      
        
          
            0
            ⁢
            
              (
              
                
                  Δ
                  ⁢
                  
                    
                  
                  ⁢
                  P
                  ⁢
                  
                    
                  
                  ⁢
                  S
                  ⁢
                  
                    
                  
                  ⁢
                  D
                
                →
                0
              
              )
            
          
          ⁢
          
            

          
          ⇒
          
            
              
                
                  N
                  r
                
                *
                Δ
                ⁢
                
                  
                
                ⁢
                P
                ⁢
                
                  
                
                ⁢
                S
                ⁢
                
                  
                
                ⁢
                D
              
              
                C
                ⁢
                
                  
                
                ⁢
                
                  L
                  H
                
              
            
            
              
                N
                ⁢
                
                  
                
                ⁢
                
                  I
                  
                    H
                    ,
                    
                      A
                      ⁢
                      
                        
                      
                      ⁢
                      n
                      ⁢
                      
                        
                      
                      ⁢
                      t
                    
                  
                
              
              +
              
                
                  
                    N
                    r
                  
                  *
                  P
                  ⁢
                  
                    
                  
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                  ⁢
                  
                    
                  
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                    D
                    
                      
                        T
                        ⁢
                        
                          
                        
                        ⁢
                        X
                      
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                        n
                        ⁢
                        
                          
                        
                        ⁢
                        t
                      
                    
                  
                
                
                  C
                  ⁢
                  
                    
                  
                  ⁢
                  
                    L
                    H
                  
                
              
            
          
        
        =
        
          
            
              
                
                  
                    2
                    *
                    Δ
                    ⁢
                    
                      
                    
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                    ⁢
                    
                      
                    
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                    C
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                        ⁢
                        
                          
                        
                      
                      I
                    
                    *
                    N
                    ⁢
                    
                      
                    
                    ⁢
                    
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                        I
                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                  
                
                
                  1
                  +
                  
                    
                      
                        N
                        r
                      
                      *
                      S
                      ⁢
                      
                        
                      
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                      ⁢
                      
                        
                      
                      ⁢
                      
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                          ,
                          
                            A
                            ⁢
                            
                              
                            
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                            n
                            ⁢
                            
                              
                            
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                            N
                            ⁢
                            
                              
                            
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                        ⁢
                        
                          
                        
                        ⁢
                        
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                            ,
                            
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                              ⁢
                              
                                
                              
                              ⁢
                              n
                              ⁢
                              
                                
                              
                              ⁢
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                      +
                      
                        Δ
                        ⁢
                        
                          
                        
                        ⁢
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                        ⁢
                        
                          
                        
                        ⁢
                        S
                        ⁢
                        
                          
                        
                        ⁢
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                        ⁢
                        
                          /
                        
                        ⁢
                        C
                        ⁢
                        
                          
                        
                        ⁢
                        
                          L
                          I
                        
                      
                    
                  
                
              
              ⁢
              
                
                  
                    N
                    r
                  
                  *
                  S
                  ⁢
                  
                    
                  
                  ⁢
                  N
                  ⁢
                  
                    
                  
                  ⁢
                  
                    R
                    
                      I
                      ,
                      
                        A
                        ⁢
                        
                          
                        
                        ⁢
                        n
                        ⁢
                        
                          
                        
                        ⁢
                        t
                      
                    
                  
                  *
                  
                    P
                    
                      
                        N
                        ⁢
                        
                          
                        
                        ⁢
                        o
                        ⁢
                        
                          
                        
                        ⁢
                        i
                        ⁢
                        
                          
                        
                        ⁢
                        s
                        ⁢
                        
                          
                        
                        ⁢
                        e
                      
                      ,
                      
                        A
                        ⁢
                        
                          
                        
                        ⁢
                        n
                        ⁢
                        
                          
                        
                        ⁢
                        t
                      
                    
                  
                
                
                  
                    N
                    ⁢
                    
                      
                    
                    ⁢
                    
                      I
                      
                        I
                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                  
                  +
                  
                    Δ
                    ⁢
                    
                      
                    
                    ⁢
                    P
                    ⁢
                    
                      
                    
                    ⁢
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                    ⁢
                    
                      
                    
                    ⁢
                    D
                    ⁢
                    
                      /
                    
                    ⁢
                    C
                    ⁢
                    
                      
                    
                    ⁢
                    
                      L
                      I
                    
                  
                
              
            
            ⁢
            
              

            
            ⇒
            
              1
              
                
                  N
                  ⁢
                  
                    
                  
                  ⁢
                  
                    I
                    
                      H
                      ,
                      
                        A
                        ⁢
                        
                          
                        
                        ⁢
                        n
                        ⁢
                        
                          
                        
                        ⁢
                        t
                      
                    
                  
                
                +
                
                  
                    
                      N
                      r
                    
                    *
                    P
                    ⁢
                    
                      
                    
                    ⁢
                    S
                    ⁢
                    
                      
                    
                    ⁢
                    
                      D
                      
                        
                          T
                          ⁢
                          
                            
                          
                          ⁢
                          X
                        
                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                  
                  
                    C
                    ⁢
                    
                      
                    
                    ⁢
                    
                      L
                      H
                    
                  
                
              
            
          
          =
          
            
              
                
                  
                    2
                    *
                    C
                    ⁢
                    
                      
                    
                    ⁢
                    
                      L
                      H
                    
                    ⁢
                    
                      /
                    
                    ⁢
                    C
                    ⁢
                    
                      
                    
                    ⁢
                    
                      L
                      I
                    
                  
                  
                    1
                    +
                    
                      
                        N
                        r
                      
                      *
                      S
                      ⁢
                      
                        
                      
                      ⁢
                      I
                      ⁢
                      
                        
                      
                      ⁢
                      N
                      ⁢
                      
                        
                      
                      ⁢
                      
                        R
                        
                          I
                          ,
                          
                            A
                            ⁢
                            
                              
                            
                            ⁢
                            n
                            ⁢
                            
                              
                            
                            ⁢
                            t
                          
                        
                      
                    
                  
                
                ⁢
                
                  
                    S
                    ⁢
                    
                      
                    
                    ⁢
                    I
                    ⁢
                    
                      
                    
                    ⁢
                    N
                    ⁢
                    
                      
                    
                    ⁢
                    
                      R
                      
                        I
                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                  
                  
                    N
                    ⁢
                    
                      
                    
                    ⁢
                    
                      I
                      
                        I
                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                  
                
              
              ⁢
              
                

              
              ⇒
              
                P
                ⁢
                
                  
                
                ⁢
                S
                ⁢
                
                  
                
                ⁢
                
                  D
                  
                    
                      T
                      ⁢
                      
                        
                      
                      ⁢
                      X
                    
                    ,
                    
                      A
                      ⁢
                      
                        
                      
                      ⁢
                      n
                      ⁢
                      
                        
                      
                      ⁢
                      t
                    
                  
                
              
            
            =
            
              
                1
                
                  N
                  r
                
              
              *
              
                {
                
                  
                    
                      C
                      ⁢
                      
                        
                      
                      ⁢
                      
                        L
                        I
                      
                      *
                      N
                      ⁢
                      
                        
                      
                      ⁢
                      
                        I
                        
                          I
                          ,
                          
                            A
                            ⁢
                            
                              
                            
                            ⁢
                            n
                            ⁢
                            
                              
                            
                            ⁢
                            t
                          
                        
                      
                      *
                      
                        (
                        
                          1
                          +
                          
                            
                              N
                              r
                            
                            *
                            S
                            ⁢
                            
                              
                            
                            ⁢
                            I
                            ⁢
                            
                              
                            
                            ⁢
                            N
                            ⁢
                            
                              
                            
                            ⁢
                            
                              R
                              
                                I
                                ,
                                
                                  A
                                  ⁢
                                  
                                    
                                  
                                  ⁢
                                  n
                                  ⁢
                                  
                                    
                                  
                                  ⁢
                                  t
                                
                              
                            
                          
                        
                        )
                      
                    
                    
                      2
                      *
                      S
                      ⁢
                      
                        
                      
                      ⁢
                      I
                      ⁢
                      
                        
                      
                      ⁢
                      N
                      ⁢
                      
                        
                      
                      ⁢
                      
                        R
                        
                          I
                          ,
                          
                            A
                            ⁢
                            
                              
                            
                            ⁢
                            n
                            ⁢
                            
                              
                            
                            ⁢
                            t
                          
                        
                      
                    
                  
                  -
                  
                    N
                    ⁢
                    
                      
                    
                    ⁢
                    
                      I
                      
                        H
                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                    *
                    C
                    ⁢
                    
                      
                    
                    ⁢
                    
                      L
                      H
                    
                  
                
                }
              
            
          
        
      
    
  




  
    
      
        
          
            ⇒
            
              S
              ⁢
              
                
              
              ⁢
              I
              ⁢
              
                
              
              ⁢
              N
              ⁢
              
                
              
              ⁢
              
                R
                
                  H
                  ,
                  
                    A
                    ⁢
                    
                      
                    
                    ⁢
                    n
                    ⁢
                    
                      
                    
                    ⁢
                    t
                  
                
              
            
          
          =
          
          ⁢
          
            
              
                
                  
                    
                      1
                      2
                    
                    *
                    
                      
                        N
                        ⁢
                        
                          
                        
                        ⁢
                        
                          I
                          
                            I
                            ,
                            
                              A
                              ⁢
                              
                                
                              
                              ⁢
                              n
                              ⁢
                              
                                
                              
                              ⁢
                              t
                            
                          
                        
                      
                      
                        N
                        ⁢
                        
                          
                        
                        ⁢
                        
                          I
                          
                            H
                            ,
                            
                              A
                              ⁢
                              
                                
                              
                              ⁢
                              n
                              ⁢
                              
                                
                              
                              ⁢
                              t
                            
                          
                        
                      
                    
                    *
                    
                      (
                      
                        1
                        +
                        
                          1
                          
                            
                              N
                              r
                            
                            *
                            S
                            ⁢
                            
                              
                            
                            ⁢
                            I
                            ⁢
                            
                              
                            
                            ⁢
                            N
                            ⁢
                            
                              
                            
                            ⁢
                            
                              R
                              
                                I
                                ,
                                
                                  A
                                  ⁢
                                  
                                    
                                  
                                  ⁢
                                  n
                                  ⁢
                                  
                                    
                                  
                                  ⁢
                                  t
                                
                              
                            
                          
                        
                      
                      )
                    
                  
                  }
                
                γ
              
              *
              
                
                  
                    
                      C
                      ⁢
                      
                        
                      
                      ⁢
                      
                        L
                        I
                      
                    
                    
                      C
                      ⁢
                      
                        
                      
                      ⁢
                      
                        L
                        H
                      
                    
                  
                  }
                
                
                  S
                  ⁢
                  
                    
                  
                  ⁢
                  I
                  ⁢
                  
                    
                  
                  ⁢
                  
                    R
                    
                      D
                      ⁢
                      
                        
                      
                      ⁢
                      L
                    
                  
                
              
            
            -
            
              1
              
                N
                r
              
            
          
        
      
    
    
      
        
          =
          
          ⁢
          
            
              γ
              *
              S
              ⁢
              
                
              
              ⁢
              I
              ⁢
              
                
              
              ⁢
              
                R
                
                  D
                  ⁢
                  
                    
                  
                  ⁢
                  L
                
              
            
            -
            
              1
              
                N
                r
              
            
          
        
      
    
  



In the case of home cell MU and virtual cell MU, the SE gain corresponds to two users and is modeled as:




  
    
      
        
          S
          ⁢
          
            
          
          ⁢
          
            E
            
              G
              ⁢
              
                
              
              ⁢
              a
              ⁢
              
                
              
              ⁢
              i
              ⁢
              
                
              
              ⁢
              n
            
          
        
        =
        
        ⁢
        
          2
          *
          
            log
            (
            
              
                1
                +
                
                  
                    
                      N
                      r
                    
                    *
                    
                      (
                      
                        
                          P
                          ⁢
                          
                            
                          
                          ⁢
                          S
                          ⁢
                          
                            
                          
                          ⁢
                          
                            D
                            
                              T
                              ⁢
                              
                                
                              
                              ⁢
                              X
                            
                          
                        
                        +
                        
                          Δ
                          ⁢
                          
                            
                          
                          ⁢
                          P
                          ⁢
                          
                            
                          
                          ⁢
                          S
                          ⁢
                          
                            
                          
                          ⁢
                          D
                        
                      
                      )
                    
                  
                  
                    C
                    ⁢
                    
                      
                    
                    ⁢
                    
                      L
                      H
                    
                    *
                    N
                    ⁢
                    
                      
                    
                    ⁢
                    
                      I
                      
                        H
                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                  
                
              
              
                1
                +
                
                  
                    
                      N
                      r
                    
                    *
                    P
                    ⁢
                    
                      
                    
                    ⁢
                    S
                    ⁢
                    
                      
                    
                    ⁢
                    
                      D
                      
                        
                          T
                          ⁢
                          
                            
                          
                          ⁢
                          X
                        
                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                  
                  
                    C
                    ⁢
                    
                      
                    
                    ⁢
                    
                      L
                      H
                    
                    *
                    N
                    ⁢
                    
                      
                    
                    ⁢
                    
                      I
                      
                        H
                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                  
                
              
            
            )
          
        
      
    
  
  
    
      
        =
        
        ⁢
        
          
            log
            (
            
              1
              +
              
                
                  
                    
                      N
                      r
                    
                    *
                    Δ
                    ⁢
                    
                      
                    
                    ⁢
                    P
                    ⁢
                    
                      
                    
                    ⁢
                    S
                    ⁢
                    
                      
                    
                    ⁢
                    D
                  
                  
                    C
                    ⁢
                    
                      
                    
                    ⁢
                    
                      L
                      H
                    
                  
                
                
                  
                    N
                    ⁢
                    
                      
                    
                    ⁢
                    
                      I
                      
                        H
                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                  
                  +
                  
                    
                      
                        N
                        r
                      
                      *
                      P
                      ⁢
                      
                        
                      
                      ⁢
                      S
                      ⁢
                      
                        
                      
                      ⁢
                      
                        D
                        
                          
                            T
                            ⁢
                            
                              
                            
                            ⁢
                            X
                          
                          ,
                          
                            A
                            ⁢
                            
                              
                            
                            ⁢
                            n
                            ⁢
                            
                              
                            
                            ⁢
                            t
                          
                        
                      
                    
                    
                      C
                      ⁢
                      
                        
                      
                      ⁢
                      
                        L
                        H
                      
                    
                  
                
              
            
            )
          
          2
        
      
    
  
  
    
      
        ≈
        
        ⁢
        
          log
          (
          
            1
            +
            
              
                2
                *
                
                  
                    
                      N
                      r
                    
                    *
                    Δ
                    ⁢
                    
                      
                    
                    ⁢
                    P
                    ⁢
                    
                      
                    
                    ⁢
                    S
                    ⁢
                    
                      
                    
                    ⁢
                    D
                  
                  
                    C
                    ⁢
                    
                      
                    
                    ⁢
                    
                      L
                      H
                    
                  
                
              
              
                
                  N
                  ⁢
                  
                    
                  
                  ⁢
                  
                    I
                    
                      H
                      ,
                      
                        A
                        ⁢
                        
                          
                        
                        ⁢
                        n
                        ⁢
                        
                          
                        
                        ⁢
                        t
                      
                    
                  
                
                +
                
                  
                    
                      N
                      r
                    
                    *
                    P
                    ⁢
                    
                      
                    
                    ⁢
                    S
                    ⁢
                    
                      
                    
                    ⁢
                    
                      D
                      
                        
                          T
                          ⁢
                          
                            
                          
                          ⁢
                          X
                        
                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                  
                  
                    C
                    ⁢
                    
                      
                    
                    ⁢
                    
                      L
                      H
                    
                  
                
              
            
          
          )
        
      
    
  




Because MU-MIMO is used in the home cell, the interference power to the virtual cell is doubled. Accordingly, the SE loss also doubled:




  
    
      
        
          S
          ⁢
          
            
          
          ⁢
          
            E
            
              L
              ⁢
              
                
              
              ⁢
              o
              ⁢
              
                
              
              ⁢
              s
              ⁢
              
                
              
              ⁢
              s
            
            I
          
        
        =
        
        ⁢
        
          2
          *
          
            log
            (
            
              
                1
                +
                
                  
                    
                      N
                      r
                    
                    *
                    S
                    ⁢
                    
                      
                    
                    ⁢
                    N
                    ⁢
                    
                      
                    
                    ⁢
                    
                      R
                      
                        I
                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                    *
                    
                      P
                      
                        
                          N
                          ⁢
                          
                            
                          
                          ⁢
                          o
                          ⁢
                          
                            
                          
                          ⁢
                          i
                          ⁢
                          
                            
                          
                          ⁢
                          s
                          ⁢
                          
                            
                          
                          ⁢
                          e
                        
                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                  
                  
                    N
                    ⁢
                    
                      
                    
                    ⁢
                    
                      I
                      
                        I
                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                  
                
              
              
                1
                +
                
                  
                    
                      N
                      r
                    
                    *
                    S
                    ⁢
                    
                      
                    
                    ⁢
                    N
                    ⁢
                    
                      
                    
                    ⁢
                    
                      R
                      
                        I
                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                    *
                    
                      P
                      
                        
                          N
                          ⁢
                          
                            
                          
                          ⁢
                          o
                          ⁢
                          
                            
                          
                          ⁢
                          i
                          ⁢
                          
                            
                          
                          ⁢
                          s
                          ⁢
                          
                            
                          
                          ⁢
                          e
                        
                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                  
                  
                    
                      N
                      ⁢
                      
                        
                      
                      ⁢
                      
                        I
                        
                          I
                          ,
                          
                            A
                            ⁢
                            
                              
                            
                            ⁢
                            n
                            ⁢
                            
                              
                            
                            ⁢
                            t
                          
                        
                      
                    
                    +
                    
                      2
                      *
                      Δ
                      ⁢
                      
                        
                      
                      ⁢
                      P
                      ⁢
                      
                        
                      
                      ⁢
                      S
                      ⁢
                      
                        
                      
                      ⁢
                      D
                      ⁢
                      
                        /
                      
                      ⁢
                      C
                      ⁢
                      
                        
                      
                      ⁢
                      
                        L
                        I
                      
                    
                  
                
              
            
            )
          
        
      
    
  
  
    
      
        =
        
        ⁢
        
          
            log
            (
            
              
                1
                +
                
                  
                    
                      N
                      r
                    
                    *
                    S
                    ⁢
                    
                      
                    
                    ⁢
                    N
                    ⁢
                    
                      
                    
                    ⁢
                    
                      R
                      
                        I
                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                    *
                    
                      P
                      
                        
                          N
                          ⁢
                          
                            
                          
                          ⁢
                          o
                          ⁢
                          
                            
                          
                          ⁢
                          i
                          ⁢
                          
                            
                          
                          ⁢
                          s
                          ⁢
                          
                            
                          
                          ⁢
                          e
                        
                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                  
                  
                    N
                    ⁢
                    
                      
                    
                    ⁢
                    
                      I
                      
                        I
                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                  
                
              
              
                1
                +
                
                  
                    
                      N
                      r
                    
                    *
                    S
                    ⁢
                    
                      
                    
                    ⁢
                    N
                    ⁢
                    
                      
                    
                    ⁢
                    
                      R
                      
                        I
                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                    *
                    
                      P
                      
                        
                          N
                          ⁢
                          
                            
                          
                          ⁢
                          o
                          ⁢
                          
                            
                          
                          ⁢
                          i
                          ⁢
                          
                            
                          
                          ⁢
                          s
                          ⁢
                          
                            
                          
                          ⁢
                          e
                        
                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                  
                  
                    
                      N
                      ⁢
                      
                        
                      
                      ⁢
                      
                        I
                        
                          I
                          ,
                          
                            A
                            ⁢
                            
                              
                            
                            ⁢
                            n
                            ⁢
                            
                              
                            
                            ⁢
                            t
                          
                        
                      
                    
                    +
                    
                      2
                      *
                      Δ
                      ⁢
                      
                        
                      
                      ⁢
                      P
                      ⁢
                      
                        
                      
                      ⁢
                      S
                      ⁢
                      
                        
                      
                      ⁢
                      D
                      ⁢
                      
                        /
                      
                      ⁢
                      C
                      ⁢
                      
                        
                      
                      ⁢
                      
                        L
                        I
                      
                    
                  
                
              
            
            )
          
          2
        
      
    
  
  
    
      
        ≈
        
        ⁢
        
          log
          (
          
            1
            +
            
              
                
                  2
                  *
                  
                    
                      2
                      *
                      Δ
                      ⁢
                      
                        
                      
                      ⁢
                      P
                      ⁢
                      
                        
                      
                      ⁢
                      S
                      ⁢
                      
                        
                      
                      ⁢
                      D
                    
                    
                      C
                      ⁢
                      
                        
                      
                      ⁢
                      
                        
                          L
                          ⁢
                          
                            
                          
                        
                        I
                      
                      *
                      N
                      ⁢
                      
                        
                      
                      ⁢
                      
                        I
                        
                          I
                          ,
                          
                            A
                            ⁢
                            
                              
                            
                            ⁢
                            n
                            ⁢
                            
                              
                            
                            ⁢
                            t
                          
                        
                      
                    
                  
                
                
                  1
                  +
                  
                    
                      
                        N
                        r
                      
                      *
                      S
                      ⁢
                      
                        
                      
                      ⁢
                      N
                      ⁢
                      
                        
                      
                      ⁢
                      
                        R
                        
                          I
                          ,
                          
                            A
                            ⁢
                            
                              
                            
                            ⁢
                            n
                            ⁢
                            
                              
                            
                            ⁢
                            t
                          
                        
                      
                      *
                      
                        P
                        
                          
                            N
                            ⁢
                            
                              
                            
                            ⁢
                            o
                            ⁢
                            
                              
                            
                            ⁢
                            i
                            ⁢
                            
                              
                            
                            ⁢
                            s
                            ⁢
                            
                              
                            
                            ⁢
                            e
                          
                          ,
                          
                            A
                            ⁢
                            
                              
                            
                            ⁢
                            n
                            ⁢
                            
                              
                            
                            ⁢
                            t
                          
                        
                      
                    
                    
                      
                        N
                        ⁢
                        
                          
                        
                        ⁢
                        
                          I
                          
                            I
                            ,
                            
                              A
                              ⁢
                              
                                
                              
                              ⁢
                              n
                              ⁢
                              
                                
                              
                              ⁢
                              t
                            
                          
                        
                      
                      +
                      
                        2
                        *
                        Δ
                        ⁢
                        
                          
                        
                        ⁢
                        P
                        ⁢
                        
                          
                        
                        ⁢
                        S
                        ⁢
                        
                          
                        
                        ⁢
                        D
                        ⁢
                        
                          /
                        
                        ⁢
                        C
                        ⁢
                        
                          
                        
                        ⁢
                        
                          L
                          I
                        
                      
                    
                  
                
              
              ⁢
              
                
                  
                    N
                    r
                  
                  *
                  S
                  ⁢
                  
                    
                  
                  ⁢
                  N
                  ⁢
                  
                    
                  
                  ⁢
                  
                    R
                    
                      I
                      ,
                      
                        A
                        ⁢
                        
                          
                        
                        ⁢
                        n
                        ⁢
                        
                          
                        
                        ⁢
                        t
                      
                    
                  
                  *
                  
                    P
                    
                      
                        N
                        ⁢
                        
                          
                        
                        ⁢
                        o
                        ⁢
                        
                          
                        
                        ⁢
                        i
                        ⁢
                        
                          
                        
                        ⁢
                        s
                        ⁢
                        
                          
                        
                        ⁢
                        e
                      
                      ,
                      
                        A
                        ⁢
                        
                          
                        
                        ⁢
                        n
                        ⁢
                        
                          
                        
                        ⁢
                        t
                      
                    
                  
                
                
                  
                    N
                    ⁢
                    
                      
                    
                    ⁢
                    
                      I
                      
                        I
                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
                          t
                        
                      
                    
                  
                  +
                  
                    2
                    *
                    Δ
                    ⁢
                    
                      
                    
                    ⁢
                    P
                    ⁢
                    
                      
                    
                    ⁢
                    S
                    ⁢
                    
                      
                    
                    ⁢
                    D
                    ⁢
                    
                      /
                    
                    ⁢
                    C
                    ⁢
                    
                      
                    
                    ⁢
                    
                      L
                      I
                    
                  
                
              
            
          
          )
        
      
    
  




Therefore, the optimal Tx power spectral density leads to signal to interference and noise ratio of equation (b):



  
    
      Δ
      ⁢
      
        
      
      ⁢
      S
      ⁢
      
        
      
      ⁢
      E
    
    =
    
      
        
          S
          ⁢
          
            
          
          ⁢
          
            E
            
              G
              ⁢
              
                
              
              ⁢
              a
              ⁢
              
                
              
              ⁢
              i
              ⁢
              
                
              
              ⁢
              n
            
          
        
        -
        
          S
          ⁢
          
            
          
          ⁢
          
            E
            
              L
              ⁢
              
                
              
              ⁢
              o
              ⁢
              
                
              
              ⁢
              s
              ⁢
              
                
              
              ⁢
              s
            
            I
          
        
      
      =
      
        
          
            0
            ⁢
            
              (
              
                
                  Δ
                  ⁢
                  
                    
                  
                  ⁢
                  P
                  ⁢
                  
                    
                  
                  ⁢
                  S
                  ⁢
                  
                    
                  
                  ⁢
                  D
                
                →
                0
              
              )
            
          
          ⁢
          
            

          
          ⇒
          
            
              2
              *
              
                
                  
                    N
                    r
                  
                  *
                  Δ
                  ⁢
                  
                    
                  
                  ⁢
                  P
                  ⁢
                  
                    
                  
                  ⁢
                  S
                  ⁢
                  
                    
                  
                  ⁢
                  D
                
                
                  C
                  ⁢
                  
                    
                  
                  ⁢
                  
                    L
                    H
                  
                
              
            
            
              
                N
                ⁢
                
                  
                
                ⁢
                
                  I
                  
                    H
                    ,
                    
                      A
                      ⁢
                      
                        
                      
                      ⁢
                      n
                      ⁢
                      
                        
                      
                      ⁢
                      t
                    
                  
                
              
              +
              
                
                  
                    N
                    r
                  
                  *
                  P
                  ⁢
                  
                    
                  
                  ⁢
                  S
                  ⁢
                  
                    
                  
                  ⁢
                  
                    D
                    
                      
                        T
                        ⁢
                        
                          
                        
                        ⁢
                        X
                      
                      ,
                      
                        A
                        ⁢
                        
                          
                        
                        ⁢
                        n
                        ⁢
                        
                          
                        
                        ⁢
                        t
                      
                    
                  
                
                
                  C
                  ⁢
                  
                    
                  
                  ⁢
                  
                    L
                    H
                  
                
              
            
          
        
        =
        
          
            
              
                
                  2
                  *
                  
                    
                      2
                      *
                      Δ
                      ⁢
                      
                        
                      
                      ⁢
                      P
                      ⁢
                      
                        
                      
                      ⁢
                      S
                      ⁢
                      
                        
                      
                      ⁢
                      D
                    
                    
                      C
                      ⁢
                      
                        
                      
                      ⁢
                      
                        
                          L
                          ⁢
                          
                            
                          
                        
                        I
                      
                      *
                      N
                      ⁢
                      
                        
                      
                      ⁢
                      
                        I
                        
                          I
                          ,
                          
                            A
                            ⁢
                            
                              
                            
                            ⁢
                            n
                            ⁢
                            
                              
                            
                            ⁢
                            t
                          
                        
                      
                    
                  
                
                
                  1
                  +
                  
                    
                      
                        N
                        r
                      
                      *
                      S
                      ⁢
                      
                        
                      
                      ⁢
                      N
                      ⁢
                      
                        
                      
                      ⁢
                      
                        R
                        
                          I
                          ,
                          
                            A
                            ⁢
                            
                              
                            
                            ⁢
                            n
                            ⁢
                            
                              
                            
                            ⁢
                            t
                          
                        
                      
                      *
                      
                        P
                        
                          
                            N
                            ⁢
                            
                              
                            
                            ⁢
                            o
                            ⁢
                            
                              
                            
                            ⁢
                            i
                            ⁢
                            
                              
                            
                            ⁢
                            s
                            ⁢
                            
                              
                            
                            ⁢
                            e
                          
                          ,
                          
                            A
                            ⁢
                            
                              
                            
                            ⁢
                            n
                            ⁢
                            
                              
                            
                            ⁢
                            t
                          
                        
                      
                    
                    
                      
                        N
                        ⁢
                        
                          
                        
                        ⁢
                        
                          I
                          
                            I
                            ,
                            
                              A
                              ⁢
                              
                                
                              
                              ⁢
                              n
                              ⁢
                              
                                
                              
                              ⁢
                              t
                            
                          
                        
                      
                      +
                      
                        2
                        *
                        Δ
                        ⁢
                        
                          
                        
                        ⁢
                        P
                        ⁢
                        
                          
                        
                        ⁢
                        S
                        ⁢
                        
                          
                        
                        ⁢
                        D
                        ⁢
                        
                          /
                        
                        ⁢
                        C
                        ⁢
                        
                          
                        
                        ⁢
                        
                          L
                          I
                        
                      
                    
                  
                
              
              ⁢
              
                
                  
                    N
                    r
                  
                  *
                  S
                  ⁢
                  
                    
                  
                  ⁢
                  N
                  ⁢
                  
                    
                  
                  ⁢
                  
                    R
                    
                      I
                      ,
                      
                        A
                        ⁢
                        
                          
                        
                        ⁢
                        n
                        ⁢
                        
                          
                        
                        ⁢
                        t
                      
                    
                  
                  *
                  
                    P
                    
                      
                        N
                        ⁢
                        
                          
                        
                        ⁢
                        o
                        ⁢
                        
                          
                        
                        ⁢
                        i
                        ⁢
                        
                          
                        
                        ⁢
                        s
                        ⁢
                        
                          
                        
                        ⁢
                        e
                      
                      ,
                      
                        A
                        ⁢
                        
                          
                        
                        ⁢
                        n
                        ⁢
                        
                          
                        
                        ⁢
                        t
                      
                    
                  
                
                
                  
                    N
                    ⁢
                    
                      
                    
                    ⁢
                    
                      I
                      
                        I
                        ,
                        
                          A
                          ⁢
                          
                            
                          
                          ⁢
                          n
                          ⁢
                          
                            
                          
                          ⁢
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Evaluation of various embodiments of uplink power control techniques using simulation results are described next. The simulation setting is listed in Table 1:







TABLE 1







Uplink System Level Simulation (SLS) Setting










Parameter
Value















Carrier frequency (GHz)
2.5
GHz



System bandwidth
10
MHz










Reuse factor
1











Frame duration
5
ms



(Preamble + DL + UL)










Number of OFDMA symbols
6



in the UL sub frame



FFT size (tone)
1024



Useful tones
864



Number of Logical
48



Resource Units (LRUs)



LRU type
CRU



Number of users per sector
10



MU-MIMO support
no











BS-to-BS distance
500
m










Channel model
eITU-Ped B, 3 km/h











Max power in MS (dBm)
23
dBm










Antenna Configuration
1 × 2 SIMO



HARQ
Synchronous, non-adaptive




HARQ with maximum




retransmission number




equal to 4



Target PER
20%



Link to system mapping
RBIR



Scheduler type
Proportional fair




scheduler











Resource Assignment
4
LRUs



Block Size



Penetration loss (dB)
20
dB










Control Overhead
25%










Table 2 summarizes simulation results based on the settings of Table 1.







TABLE 2







Simulation Results












Sector
Cell-edge user




Gamma
throughput
throughput
Sector
Cell-Edge


value
(in Mbps)
(in Kbps)
SE
user SE














0.2
1.3865
104
0.8146
0.0611


0.4
1.5655
95.6
0.9198
0.0562


0.6
1.7056
77.2
1.002
0.0454


0.8
1.7895
58.8
1.0514
0.0345


1.0
1.8619
41.2
1.0939
0.0242









FIG. 6 depicts a cumulative density function (CDF) of user throughput. FIGS. 7A and 7B depict performance curve and interference over thermal control curve for some simulation results for the simulation results of Table 2.
Based on the presented simulation results, various embodiments provide benefit for the uplink of: (1) interference control and (2) tradeoff between of overall system throughput and cell edge performance.
It is noted that the power control scheme of various embodiments can meet the 802.16m requirements for the cell-edge user performance without appreciable degradation of the average spectral efficiency.
Embodiments of the present invention may be implemented as any or a combination of: one or more microchips or integrated circuits interconnected using a motherboard, hardwired logic, software stored by a memory device and executed by a microprocessor, firmware, an application specific integrated circuit (ASIC), and/or a field programmable gate array (FPGA). The term “logic” may include, by way of example, software or hardware and/or combinations of software and hardware.
Embodiments of the present invention may be provided, for example, as a computer program product which may include one or more machine-readable media having stored thereon machine-executable instructions that, when executed by one or more machines such as a computer, network of computers, or other electronic devices, may result in the one or more machines carrying out operations in accordance with embodiments of the present invention. A machine-readable medium may include, but is not limited to, floppy diskettes, optical disks, CD-ROMs (Compact Disc-Read Only Memories), and magneto-optical disks, ROMs (Read Only Memories), RAMs (Random Access Memories), EPROMs (Erasable Programmable Read Only Memories), EEPROMs (Electrically Erasable Programmable Read Only Memories), magnetic or optical cards, flash memory, or other type of media/machine-readable medium suitable for storing machine-executable instructions.
The drawings and the forgoing description gave examples of the present invention. Although depicted as a number of disparate functional items, those skilled in the art will appreciate that one or more of such elements may well be combined into single functional elements. Alternatively, certain elements may be split into multiple functional elements. Elements from one embodiment may be added to another embodiment. For example, orders of processes described herein may be changed and are not limited to the manner described herein. Moreover, the actions of any flow diagram need not be implemented in the order shown; nor do all of the acts necessarily need to be performed. Also, those acts that are not dependent on other acts may be performed in parallel with the other acts. The scope of the present invention, however, is by no means limited by these specific examples. Numerous variations, whether explicitly given in the specification or not, such as differences in structure, dimension, and use of material, are possible. The scope of the invention is at least as broad as given by the following claims.

## Claims

1. A mobile station comprising:
logic to receive, from a base station, a control factor determined from neighboring base station uplink interference levels for multiple-user multi-input multi-output (MU-MIMO) operations, a minimum signal to interference and noise ratio, a noise plus interference level information, a downlink preamble, and a Base Station Effective Isotropic Radiated Power (BS_EIRP) parameter;
logic to determine estimated average uplink propagation loss from the downlink preamble and the BS_EIRP parameter received from the base station; and
logic to determine an uplink transmit power per antenna using an open loop transmission power control calculation formula based in part on the control factor, minimum signal to interference and noise ratio, noise plus interference level information, and the estimate average uplink propagation loss.

2. The mobile station of claim 1, wherein the logic to determine an uplink transmit power per antenna is to determine:


P(dBm)=L+SINRTarget+NI,

where L comprises the estimated average uplink propagation loss, SINRTarget comprises a target signal to interference and noise ratio, and NI comprises an estimated average power level of noise and interference per subcarrier of at least one base station.

3. The mobile station of claim 1, wherein the logic to determine an uplink transmit power per antenna is to determine:


P(dBm)=L+SINRTarget+NI+Offset_AMSperAMS+Offset_ABSperAMS,

where L comprises the estimated average uplink propagation loss, SINRTarget comprises a target uplink signal to interference and noise ratio (SINR) received by an advanced base station (ABS), NI comprises estimated average power level of noise and interference per subcarrier at the ABS, not including ABS's receive antenna gain, Offset_AMSperAMS comprises a correction term for AMS-specific power offset, and Offset_ABSperAMS comprises a correction term for AMS-specific power offset.

4. The mobile station of claim 3, wherein:
the SINRTarget is based at least in part on:





  
    SINR
    Target
  
  =
  
    {
    
      
        
          
            
              
                
                  C
                  /
                  N
                
                -
                
                  10
                  ⁢
                  
                    
                  
                  ⁢
                  log
                  ⁢
                  
                    
                  
                  ⁢
                  10
                  ⁢
                  
                    
                  
                  ⁢
                  
                    (
                    R
                    )
                  
                
              
              ,
            
          
          
            
              mode
              ⁢
              
                
              
              ⁢
              1
            
          
        
        
          
            
              
                SINR
                OPT
              
              ,
            
          
          
            
              mode
              ⁢
              
                
              
              ⁢
              2
            
          
        
      
      ,
    
  



where
C/N comprises a normalized carrier-to-noise ratio of a modulation/FEC rate for a current transmission, R comprises a number of repetitions for the modulation/FEC rate, and SINROPT comprises a target SNR value for interference over thermal control;
wherein the control factor identifies mode 1 or mode 2 for use in calculating the SINRTarget.

5. The mobile station of claim 3, wherein:
the SINRTarget is based at least in part on:





  
    
      SINR
      Target
    
    =
    
      10
      ⁢
      
        
      
      ⁢
      log
      ⁢
      
        
      
      ⁢
      10
      ⁢
      
        (
        
          max
          (
          
            
              
                10
                ⋀
              
              ⁢
              
                (
                
                  
                    SINR
                    MIN
                  
                  10
                
                )
              
            
            ,
            
              
                γ
                ×
                
                  SINR
                  DL
                
              
              -
              
                1
                
                  N
                  r
                
              
            
          
          )
        
        )
      
    
  
  ,



where γ represents the control factor and comprises a fairness and interference over thermal (IoT) control factor, SINRDL comprises a ratio of useful downlink signal to downlink interference power measured at the mobile station, and Nr comprises the number of receive antennas at the base station in communication with the mobile station.

6. The mobile station of claim 5, wherein:
the IoT control factor is based at least in-part on uplink interference level of neighboring base stations.

7. A method, comprising:
receiving, from a base station, a control factor determined from neighboring base station uplink interference levels for multiple-user multi-input multi-output (MU-MIMO) operations, minimum signal to interference and noise ratio, a noise plus interference level information, a downlink preamble, and a Base Station Effective Isotropic Radiated Power (BS_EIRP) parameter;
determining an estimated average uplink propagation loss from the downlink preamble and the BS_EIRP parameter received from the base station; and
determining an uplink transmit power per antenna using an open loop transmission power control calculation formula based in part on the control factor, minimum signal to interference and noise ratio, noise plus interference level information, and the estimated average uplink propagation loss.

8. The method of claim 7, wherein the determining the uplink transmit power per antenna further comprises determining an uplink transmit power per antenna according to:


P(dBm)=L+SINRTarget+NI,

where
L comprises the estimated average uplink propagation loss, SINRTarget comprises a target signal to interference and noise ratio, and NI comprises an estimated average power level of noise and interference per subcarrier of at least one base station.

9. The method of claim 7, wherein the determining the uplink transmit power per antenna further comprises determining an uplink transmit power per antenna according to:


P(dBm)=L+SINRTarget+NI+Offset_AMSperAMS+Offset_ABSperAMS,

where
L comprises the estimated average uplink propagation loss, SINRTarget comprises a target uplink signal to interference and noise ratio (SINR) received by an advanced base station (ABS), NI comprises estimated average power level of noise and interference per subcarrier at the ABS, not including ABS's receive antenna gain, Offset_AMSperAMS comprises a correction term for AMS-specific power offset, and Offset_ABSperAMS comprises a correction term for AMS-specific power offset.

10. The method of claim 9, wherein the determining the uplink transmit power per antenna further comprises determining the SINRTarget based at least in part on:




  
    
  
  ⁢
  
    
      
        SINR
        Target
      
      =
      
        10
        ⁢
        
          
        
        ⁢
        log
        ⁢
        
          
        
        ⁢
        10
        ⁢
        
          (
          
            max
            (
            
              
                
                  10
                  ⋀
                
                ⁢
                
                  (
                  
                    
                      SINR
                      MIN
                    
                    10
                  
                  )
                
              
              ,
              
                
                  γ
                  ×
                  
                    SINR
                    DL
                  
                
                -
                
                  1
                  
                    N
                    r
                  
                
              
            
            )
          
          )
        
      
    
    ,
  



where γ represents the control factor and comprises a fairness and interference over thermal (IoT) control factor, SINRDL comprises a ratio of useful downlink signal to downlink interference power measured at the mobile station, and Nr comprises the number of receive antennas at the base station in communication with the mobile station.

11. The method of claim 10, wherein the determining the SINRTarget further comprises determining the SINRTarget using the IoT control factor based at least in-part on uplink interference level of neighboring base stations.

12. The method of claim 9, wherein the determining the SINRTarget further comprises determining the SINRTarget is based at least in part on:




  
    SINR
    Target
  
  =
  
    {
    
      
        
          
            
              
                
                  C
                  /
                  N
                
                -
                
                  10
                  ⁢
                  
                    
                  
                  ⁢
                  log
                  ⁢
                  
                    
                  
                  ⁢
                  10
                  ⁢
                  
                    
                  
                  ⁢
                  
                    (
                    R
                    )
                  
                
              
              ,
            
          
          
            
              mode
              ⁢
              
                
              
              ⁢
              1
            
          
        
        
          
            
              
                SINR
                OPT
              
              ,
            
          
          
            
              mode
              ⁢
              
                
              
              ⁢
              2
            
          
        
      
      ,
    
  



where
C/N comprises a normalized carrier-to-noise ratio of a modulation/FEC rate for a current transmission, R comprises a number of repetitions for the modulation/FEC rate,

and SINROPT comprises a target SINR value for interference over thermal control;
wherein the control factor identifies mode 1 or mode 2 for use in calculating the SINRTarget.

13. A system comprising:
at least one antenna communicatively coupled to abuse station,
a computer system communicatively coupled to the at least one antenna, le compute system comprising:
logic to receive, from the base station, a control factor determined from neighboring base station uplink interference levels for multiple-user multi-input multi-output (MU-MIMO) operations, a minimum signal to interference and noise ratio, a noise plus interference level information, a downlink preamble, and a Base Station Effective Isotropic Radiated Power (BS_EIRP) parameter;
logic to determine an estimated average uplink propagation loss from the downlink preamble and the BS_EIRP parameter received from the base station; and
logic to determine an uplink transmit power per antenna using an open loop transmission power control calculation formula based in part on the control factor, minimum signal to interference and noise ratio, noise plus interference level information, and the estimate average uplink propagation loss.

14. The system of claim 13, wherein the logic to determine an uplink transmit power per antenna is to determine:


P(dBm)=L+SINRTarget+NI,

where L comprises the estimated average uplink propagation loss, SINRTarget comprises a target signal to interference and noise ratio, and NI comprises an estimated average power level of noise and interference per subcarrier of at least one base station.

15. The mobile station-system of claim 13, wherein the logic to determine an uplink transmit power per antenna is to determine:


P(dBm)=L+SINRTarget+NI+Offset_AMSperAMS+Offset_ABSperAMS,

where L comprises the estimated average uplink propagation loss, SINRTarget comprises a target uplink signal to interference and noise ratio (SINR) received by an advanced base station (ABS), NI comprises estimated average power level of noise and interference per subcarrier at the ABS, not including ABS's receive antenna gain, Offset_AMSperAMS comprises a correction term for AMS-specific power offset, and Offset_ABSperAMS comprises a correction term for AMS-specific power offset.