# Patent

## Title
Grant utilization based other cell interference estimation

## Abstract

Mobile broadband traffic has been exploding in wireless networks resulting in an increase of interferences and reduced operator control. Networks are also becoming more heterogeneous putting additional demand in interference management. Scheduler schedules uplink transmissions from UEs based on a load prediction algorithm that typically assumes worst case. However, UEs do not always use full power granted, and thus, much of granted radio resources are wasted. To address these and other issues, technique(s) to accurately predict/estimate other cell interferences and thermal noise separately and to accurately predict/estimate grant utilization probability and variance is(are) described. Inventive estimation technique(s) can be used to schedule UEs to more fully utilize available radio resources. Extended Kalman filtering can be adapted for use in estimation providing low order computational complexity.

## Background
RELATED APPLICATION
This application may be related, at least in part, to U.S. application Ser. No. 13/488,187 entitled “OTHER CELL INTERFERENCE ESTIMATION” filed Jun. 4, 2012; and to U.S. application Ser. No. 13/656,581 entitled “METHOD, APPARATUS, AND SYSTEM FOR INTERFERENCE AND NOISE ESTIMATION” filed Oct. 12, 2012, the entire contents of which are hereby incorporated by reference.
TECHNICAL FIELD
The technical field of the present disclosure generally relates to estimating other cell interferences in a wireless network. In particular, the technical field relates to apparatus(es), method(s), and/or system(s) for estimating other cell interferences using grant utilizations.
BACKGROUND
Recently, at least the following trends have emerged in field of cellular telephony. First, mobile broadband traffic has been exploding in wireless networks such as WCDMA (wideband code division multiple access). The technical consequence is a corresponding steep increase of the interference in these networks, or equivalently, a steep increase of the load. This makes it important to exploit the load headroom that is left in the most efficient way.
Second, cellular networks are becoming more heterogeneous, with macro RBSs (radio base station) being supported by micro and pico RBSs at traffic hot spots. Furthermore, home base stations (e.g., femto RBSs) are emerging in many networks. This trend puts increasing demands on inter-cell interference management.
Third, the consequence of the above is a large increase of the number of network nodes in cellular networks, together with a reduced operator control. There is therefore a strong desire to introduce more self-organizing network (SON) functionality. Such functionality may support interference management by automatic interference threshold setting and adaptation, for a subset of the nodes of the cellular network.
As a result, there are problems that can hinder providing efficient service. In WCDMA for example, the UEs (user equipments) may or may not utilize the power granted by the EUL (enhanced uplink) scheduler. This leads to an inaccuracy of the load prediction step, where the scheduler bases its scheduling decision on a prediction of the resulting air interface load of the traffic it schedules. This is so since the 3GPP standard has an inherent delay of about 5 TTIs (transmission time interval) from the scheduling decision until the interference power appears over the air interface. Also the WCDMA load prediction does not account for all imperfections in the modeling of an UL (uplink) radio receiver. This can lead to additional inaccuracies in the load prediction and estimation steps.
The inventor is not aware of readily available any practical cell interference estimation algorithm that can provide other cell interference estimates with an inaccuracy better than 10-20%, and does so with close to transmission time interval (TTI, typically 2 ms or 10 ms) bandwidth (typically 250 or 50 Hz) over the power and load ranges of interest. As a result, it is not possible to make optimal scheduling decisions since the exact origin of the interference power in the UL is unknown.
Load Estimation without Other Cell Interference Estimation
Following is a discussion on measurement and estimation techniques to measure instantaneous total load on the uplink air interface given in a cell of a WCDMA system. In general, a load at the antenna connector is given by noise rise, also referred to as rise over thermal, RoT(t), defined by:




  
    
      
        
          
            RoT
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where PN(t) is the thermal noise level as measured at the antenna connector. For the purposes of discussion, PRTWP(t) may be viewed as the total wideband power defined by:





  
    
      
        
          
            
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also measured at the antenna connector. The total wideband power PRTWP(t), is unaffected by any de-spreading applied. In (2), Pother(t) represents the power as received from one or more cells of the WCDMA system other than an own cell. The Pi(t) are the powers of the individual users. One major difficulty of any RoT estimation technique is in the inherent inability to separate the thermal noise PN(t) from the interference Pother(t) from other cells.

Another specific problem that needs to be addressed is that the signal reference points are, by definition, at the antenna connectors. The measurements are however obtained after the analog signal conditioning chain, in the digital receiver. The analog signal conditioning chain introduces a scale factor error of about 1 dB (1-sigma) that is difficult to compensate for. Fortunately, all powers of (2) are equally affected by the scale factor error so when (1) is calculated, the scale factor error is cancelled as follows:




  
    
      
        
          
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To understand the fundamental problem of interferences from other cells when performing load estimation, note that:

Pother(t)+PN(t)=E[Pother(t)]+E[PN(t)]+ΔPother(t)+ΔPN(t).  (4)

where E[ ] denotes a mathematical expectation and where Δ denotes a variation around the mean. The fundamental problem can now be clearly seen. Since there are no measurements available in the RBS that are related to the other cell interference, a linear filtering operation can at best estimate the sum E[Pother(t)]+E[PN(t)]. This estimate cannot be used to deduce the value of E[PN(t)]. The situation is the same as when only the sum of two numbers is available. Then there is no way to figure out the individual values of E[Pother(t)] and E[PN(t)]. It has also been formally proved that the thermal noise power floor is not mathematically observable in case there is a non-zero mean other cell interference present in the uplink (UL).

FIG. 1 illustrates a conventional algorithm that estimates a noise floor. The illustrated algorithm is referred to as a sliding window algorithm, and estimates the RoT as given by equation (1). The main problem solved by this conventional estimation algorithm is that it can provide an accurate estimation of the thermal noise floor N(t). Since it is not possible to obtain exact estimates of this quantity due to the other cell interference, the estimator therefore applies an approximation, by consideration of a soft minimum as computed over a relative long window in time. It is important to understand that this estimation relies on the fact that the noise floor is constant over very long periods of time (disregarding the small temperature drift).
One significant disadvantage of the sliding window algorithm is that the algorithm requires a large amount of storage memory. This becomes particularly troublesome in case a large number of instances of the algorithm is needed, as may be the case when base stations serve many cells and when techniques like 4-way receiver diversity is introduced in the WCDMA UL. A recursive algorithm has been introduced to reduce the memory consumption. Relative to the sliding window algorithm, the recursive algorithm can reduce the memory requirement by a factor of more than one hundred.
Load Prediction without Interference Power Estimation
Following is a discussion on techniques to predict instantaneous load on the uplink air interface ahead in time. The scheduler uses this functionality. The scheduler tests different combinations of grants to determine the best combinations, e.g., maximizing the throughput. This scheduling decision will only affects the air interface load after a number of TTIs (each such TTI a predetermined time duration such as 2 or 10 ms), due to grant transmission latency and UE latency before the new grant takes effect over the air interface.
In a conventional SIR (signal-to-interference ratio) based method, the prediction of uplink load, for a tentative scheduled set of UEs and grants, is based on the power relation defined by:




  
    
      
        
          
            
              
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        (
        5
        )
      
    
  




where Li(t) is the load factor of the i-th UE of the own cell. As indicated, Pother(t) denotes the other cell interference. The load factors of the own cell are computed as follows. First, note that:





  
    
      
        
          
            
              
                
                  
                    
                      
                        
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where I is the number of UEs in the own cell and α is the self-interference factor. The carrier to interference values, (C/I)i(t), i=1, . . . , I, are then related to the SINR (measured on the DPCCH channel) as follows:





  
    
      
        
          
            
              
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In (7), Wi represents the spreading factor, RxLoss represents the missed receiver energy, G represents the diversity gain and the β:s represent the beta factors of the respective channels. Here, inactive data channels are assumed to have zero data beta factors.
The UL load prediction then computes the uplink load of the own cell by a calculation of (6) and (7) for each UE of the own cell, followed by a summation:




  
    
      
        
          
            
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which transforms (5) to:

PRTWP(t)=Lown(t)PRTWP(t)+Pother(t)+PN(t).  (9)

Dividing (9) by PN(t) shows that the RoT can be predicted k TTIs ahead as:





  
    
      
        
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In the SIR based load factor calculation, the load factor Li(t) is defined by (6). However, in a power based load factor calculation, the load factor Li(t) can be defined by:




  
    
      
        
          
            
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              i
            
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              (
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                i
              
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        I
        ,
      
    
    
      
        (
        11
        )
      
    
  




and equations (8)-(10) may be calculated based on the load factor Li(t) of (11) to predict the RoT k TTIs ahead. An advantage of the power based load factor calculation is that the parameter dependency is reduced. But on the downside, a measurement of the UE power is needed. Older HW may continue to rely on (5)-(10).

In heterogeneous networks (HetNets), different kinds of cells are mixed. A problem that arises in Hetnets in that the cells are likely to have different radio properties in terms of (among others):
radio sensitivity;
frequency band;
coverage;
output power;
capacity; and
acceptable load level.
This can be an effect of the use of different RBS sizes (macro, micro, pico, femto), different revisions (different receiver technology, SW quality), different vendors, the purpose of a specific deployment, and so on. An important factor in HetNets is that of the air interface load management, i.e., the issues associated with the scheduling of radio resources in different cells and the interaction between cells in terms of inter-cell interference.
These issues are exemplified with reference to FIG. 2 which illustrates a low power cell with limited coverage intended to serve a hotspot. To enable sufficient coverage of the hot spot, an interference suppressing receiver like the G-rake+ is used. One problem is now that the low power cell is located in the interior of and at the boundary of a specific macro cell. Also, surrounding macro cells interfere with the low power cell rendering a high level of other cell interference in the low power cell which, despite the advanced receiver, reduces the coverage to levels that do not allow coverage of the hot spot. As a result, UEs of the hot spot are connected to the surrounding macro cells, which can further increase the other cell interference experienced by the low power cell.
As mentioned, scheduling decisions may be made based on a prediction of air interface load (e.g., RoT) that will result due to the scheduled grants to ensure that scheduled load does not exceed the load thresholds for coverage and stability. If the load prediction is made assuming the worst case (that all UEs use all granted resources at all times), it can lead to a waste of air-interface resources since the UEs are not required to use all granted resources. Thus, it is desirable to estimate and predict the load accurately so as to minimize waste of resources.
SUMMARY
In one or more aspects of the disclosed subject matter, it is proposed that by accurately determining interferences experienced at an own cell, and in particular, by accurately determining interferences at the own cell due to activities of other cells, the load can be accurately estimated and predicted. In addition, one or more of the proposed solutions enable the determination of the other cell interferences at or near the bandwidth of the scheduling decisions.
A non-limiting aspect of the disclosed subject matter is directed to a method performed in a radio network node of a wireless network for determining other cell interference applicable at a particular time. The method can comprise the step of estimating (710) a grant utilization probability pgrant(t1) based at least on a grant utilization probability estimate {circumflex over (p)}grant(t0) and an interference-and-noise sum estimate {circumflex over (P)}other(t0)+{circumflex over (P)}N(t0) applicable at a time t0 to obtain a grant utilization probability estimate {circumflex over (p)}grant(t1) applicable at a time t1, in which t1−t0=T>0. The method can also comprise the step of estimating an interference-and-noise sum Pother(t1)+PN(t1) based at least on the grant utilization probability estimate {circumflex over (p)}grant(t0) and the interference-and-noise sum estimate {circumflex over (P)}other(t0)+{circumflex over (P)}N(t0) to obtain an interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) applicable at the time t1. The method can further comprise the step of estimating an other cell interference Pother(t1) based at least on the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) and a thermal noise estimate {circumflex over (P)}N(t1) to obtain an other cell interference estimate {circumflex over (P)}other(t1) applicable at the time t1.
Another non-limiting aspect of the disclosed subject matter is directed to a computer-readable medium which has programming instructions. When a computer executes the programming instructions, the computer executes the method performed in a radio network node of a wireless network as described above for determining other cell interference applicable at a particular time.
Yet another non-limiting aspect of the disclosed subject matter is directed to a radio network node of a wireless network. The radio network node is structured to determine other cell interference applicable at a particular time. The radio network node can comprise a transceiver structured to transmit and receive wireless signals via one or more antennas from and to one or more cell terminals located within the cell of interest, a communicator structured to communicate with other network nodes, and a scheduler structured to schedule uplink transmissions from the cell terminals. The scheduler can also be structured to estimate a grant utilization probability pgrant(t1) based at least on a grant utilization probability estimate {circumflex over (p)}grant(t0) and an interference-and-noise sum estimate {circumflex over (P)}other(t0)+{circumflex over (P)}N(t0) applicable at a time t0 to obtain a grant utilization probability estimate {circumflex over (p)}grant(t1) applicable at a time t1, wherein t1−t0=T>0. The scheduler can further be structured to estimate an interference-and-noise sum Pother(t1)+PN(t1) based at least on the grant utilization probability estimate {circumflex over (p)}grant(t0) and the interference-and-noise sum estimate {circumflex over (P)}other(t0)+{circumflex over (P)}N(t0) to obtain an interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) applicable at the time t1. The scheduler can yet further be structured to estimate an other cell interference Pother(t1) based at least on the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) and a thermal noise estimate {circumflex over (P)}N(t1) to obtain an other cell interference estimate {circumflex over (P)}other(t1) applicable at the time t1.
In these aspects, the grant utilization probability pgrant(t) can express a relationships between radio resource grants scheduled to one or more cell terminals and radio resource grants used by the same cell terminals applicable at a time t. Each cell terminal can be a wireless terminal in the cell of interest, and {circumflex over (p)}grant(t) can express an estimate of the grant utilization probability pgrant(t). The interference-and-noise sum Pother(t)+PN(t) can express a sum of undesired signals, other than an own cell load Pown(t), applicable at the time t, and {circumflex over (P)}other(t)+{circumflex over (P)}N(t) can express an estimate of the interference-and-noise sum estimate Pother(t)+PN(t). The own cell load Pown(t) can express a sum of signals due to wireless activities in the cell of interest. The other cell interference Pother(t) can express a sum of interferences present in the cell of interest due to wireless activities applicable at the time t in one or more cells other than in the cell of interest, and {circumflex over (P)}other(t) can express an estimate of the other cell interference Pother(t). A thermal noise PN(t) can express a sum of undesired signals present in the cell of interest at the time t other than the own cell load Pown(t) and other than the other cell interference Pother(t), and {circumflex over (P)}N(t1) can express an estimate of the thermal noise PN(t).



DESCRIPTION OF THE DRAWINGS
The foregoing and other objects, features, and advantages of the disclosed subject matter will be apparent from the following more particular description of preferred embodiments as illustrated in the accompanying drawings in which reference characters refer to the same parts throughout the various views. The drawings are not necessarily to scale.
FIG. 1 illustrates a conventional algorithm that estimates a noise floor;
FIG. 2 illustrates an example scenario of a low power cell with limited coverage intended to serve a hotspot;
FIG. 3 illustrates a plot of a grant utilization probability;
FIG. 4 illustrates an example scenario in which other cell interference is determined;
FIGS. 5 and 6 respectively illustrate example embodiments of a radio network node;
FIG. 7 illustrates a flow chart of example method performed by a radio network node to determine an other cell interference;
FIG. 8 illustrates a flow chart of an example process performed by a radio network node to estimate the grant utilization probability and to estimate the interference-and-noise sum;
FIG. 9 illustrates a flow chart of another example process performed by a radio network node to estimate the grant utilization probability and to estimate the interference-and-noise sum;
FIG. 10 illustrates a flow chart of an example process performed by a radio network node to obtain an interference-and-noise sum estimate;
FIG. 11 illustrates a flow chart of an example process performed by a radio network node to determine an other cell interference estimate;
FIG. 12 illustrates a flow chart of yet another example process performed by a radio network node to estimate the grant utilization probability and to estimate the interference-and-noise sum; and
FIG. 13 illustrates a flow chart of an example process performed by a radio network node to perform an (extended) Kalman filter update of a predicted state vector.



DETAILED DESCRIPTION
For purposes of explanation and not limitation, specific details are set forth such as particular architectures, interfaces, techniques, and so on. However, it will be apparent to those skilled in the art that the technology described herein may be practiced in other embodiments that depart from these specific details. That is, those skilled in the art will be able to devise various arrangements which, although not explicitly described or shown herein, embody the principles of the described technology.
In some instances, detailed descriptions of well-known devices, circuits, and methods are omitted so as not to obscure the description with unnecessary details. All statements herein reciting principles, aspects, embodiments and examples are intended to encompass both structural and functional equivalents. Additionally, it is intended that such equivalents include both currently known equivalents as well as equivalents developed in the future, i.e., any elements developed that perform same function, regardless of structure.
Thus, for example, it will be appreciated that block diagrams herein can represent conceptual views of illustrative circuitry embodying principles of the technology. Similarly, it will be appreciated that any flow charts, state transition diagrams, pseudo code, and the like represent various processes which may be substantially represented in computer readable medium and executed by a computer or processor, whether or not such computer or processor is explicitly shown.
Functions of various elements including functional blocks labeled or described as “processors” or “controllers” may be provided through dedicated hardware as well as hardware capable of executing associated software. When provided by a processor, functions may be provided by a single dedicated processor, by a single shared processor, or by a plurality of individual processors, some of which may be shared or distributed. Moreover, explicit use of term “processor” or “controller” should not be construed to refer exclusively to hardware capable of executing software, and may include, without limitation, digital signal processor (shortened to “DSP”) hardware, read only memory (shortened to “ROM”) for storing software, random access memory (shortened to RAM), and non-volatile storage.
In this document, 3GPP terminologies—e.g., WCDMA, LTE—are used as examples for explanation purposes. Note that the technology described herein can be applied to non-3GPP standards, e.g., WiMAX, cdma2000, 1xEVDO, etc. Thus, the scope of this disclosure is not limited to the set of 3GPP wireless network systems and can encompass many domains of wireless network systems. Also, a base station (e.g., RBS, NodeB, eNodeB, eNB, etc.) will be used as an example of a radio network node in which the described method can be performed. However, it should be noted that the disclosed subject matter is applicable to any node, such as relay stations, that receive wireless signals. Also without loss of generality, mobile terminals (e.g., UE, mobile computer, PDA, etc.) will be used as examples of wireless terminals that communicate with the base station.
As indicated above, one major disadvantage of many conventional RoT(t) estimation techniques is in the difficulty in separating the thermal noise PN(t) from the interference Pother(t) from other cells. This makes it difficult to estimate the RoT(t), i.e., difficult to estimate the load as given in equation (1). The other cell interference Pother(t) in this context may be viewed as a sum of interferences present in a cell of interest due to wireless activities applicable at time t in one or more cells other than in the cell of interest. In one or more aspects, the determination of the other cell interference Pother(t) involves estimating the other cell interference. For the purposes of this disclosure, estimations of parameters are indicated with a “^” (caret) character. For example, {circumflex over (P)}other(t) may be read as an estimate of the other cell interference Pother(t).
There are known techniques to determine the other cell interference estimate {circumflex over (P)}other(t). These conventional techniques assume that the powers of all radio links are measured in the uplink receiver. This assumption is not true in many instances today. The power measurement is associated with difficulties since:

    
    
        In WCDMA for example, the uplink transmission is not necessarily orthogonal, which can cause errors when the powers are estimated;
        The individual code powers are often small, making the SNRs (signal-to noise ratio) low as well. This further contributes to the inaccuracy of the power estimates.
    
    


One major problem associated with the conventional other cell interference estimation techniques is that the sum of other cell interference and thermal noise Pother(t)+PN(t)(referred to as the interference-and-noise sum) needs to be estimated through high order Kalman filtering. The primary reason is that all powers of the UEs need to be separately filtered using at least one Kalman filter state per UE when such techniques are used. This step therefore is associated with a very high computational complexity. There are techniques that can reduce this computational complexity, but the complexity can be still too high when the number of UEs increases. In these conventional solutions, the thermal noise floor N(t) is estimated as described above, i.e., {circumflex over (N)}(t) is determined followed by a subtraction to arrive at an estimate of the other cell interference {circumflex over (P)}other(t).
In the existing solutions, the EUL utilizes a scheduler that aims to fill the load headroom of the air interface, so that the different UE requests for bitrates are met. As stated above, the air-interface load in WCDMA is determined in terms of the noise rise over the thermal power level, i.e., the RoT(t), which is estimated at the base station.
When evaluating scheduling decisions, the scheduler predicts the load that results form the scheduled grants, to make sure that the scheduled load does not exceed the load thresholds for coverage and stability. This can be complicated since the grant given to a UE only expresses a limit on the UL power the UE is allowed to use. However, the UE may actually use only a portion of its grant. The conventional scheduler often has to make a worst case analysis, assuming that all UEs will use their grants at all times. But in reality, UEs in general have a relatively low utilization of grants. This is evident from field measurements as those depicted in FIG. 3. The plot indicates a grant utilization of only about 25%. In other words, a significant amount (about 75%) of air-interface resources is wasted.
To summarize, there is a lack of technology that can estimate the other cell interference with sufficient accuracy (e.g., within 10-20%), sufficiently close in time (e.g., with close to TTI bandwidth) over the power and ranges of interest. There is also a lack of other cell interference estimation technology that accounts for a high bandwidth measured grant utilization probability. The consequence is that it is not possible to make optimal scheduling decisions since the exact origin of the interference power in the UL is not known with a sufficient accuracy and bandwidth. Furthermore, it is not possible to manage interference in heterogeneous networks (HetNets) in an optimal way. This follows since different actions are needed depending on the origin of the interference power. This is easily understood in overload situations, since then the correct cell needs to receive power down commands e.g. in the form of reduced thresholds to resolve the situation.
Regarding HetNets in particular, problems associated with conventional scheduling techniques can be explained in a relatively straightforward manner. For scheduling in the base station in general, prior techniques require measurement of all UE powers in the UL. This is very costly computationally, requiring Kalman filters of high order for processing the measurements to obtain estimates of the other cell interference power. This is because each own cell UE adds a state to the Kalman filter. The consequence, if such estimation cannot be done, is that the scheduler is unaware of the origin of the interference, thereby making it more difficult to arrive at good scheduling decisions. For HetNets, the problem is again that there is no information of the origin of interference, and interference variance, for adjacent cells. This is primarily due to the lack of low complexity estimators for these quantities.
Each of one or more aspects of the disclosed subject matter addresses one or more of the issues related to conventional techniques. For example, recall from above that in conventional scheduling techniques, there is a delay of some number of TTIs from the scheduling decision until the interference power appears over the air interface. The scheduler also bases its scheduling decisions on a prediction of the load of the traffic it schedules. Since the UEs do not always utilize power granted by the scheduler, the load prediction are likely to be inaccurate. The inaccuracy tends to increase as the delay increases.
A general concept applicable to one or more inventive aspects includes an algorithm to estimate other cell interferences. The algorithm may run in the RBS base band. The algorithm may be implemented any network node (e.g., RBS, RNC, CN, etc.) or any combination. An estimator implementing the other cell interference estimation algorithm may estimate the sum of all other cell interferences, experienced in the own cell context. The estimator may be responsive to:

    
    
        Grant utilization (which may be measured, computed)
        Total wideband received uplink power (which may be measured)
        Own cell load (which may be computed, scheduled), directly related to grants.
    
    


In this discussion, the values of parameters are “estimated”, “measured”, “received” or “computed”. A measured value in essence can be viewed a number that expresses a value of a measured quantity. An estimated value is not a number that expresses a value of a measurement, at least not directly. Rather, an estimate can be viewed as a processed set of measurements, e.g., by some filtering operation. There can also be received and/or computed quantities, such as time varying parameters that are obtained from other sources. It is stressed that measured or estimated quantities can be very different, also in case the measured and estimated quantity refer to the same underlying physical quantity, e.g., a specific power. One among many reasons for this is that the processing to obtain estimates e.g., may combine measurements from different times to achieve e.g., noise suppression and bias reduction.
As will be demonstrated below, one very significant advantage of the inventive estimator is its low order and associated low computational complexity. In one embodiment, the estimator can be a variant of an extended Kalman filter (EKF), arranged for processing using the nonlinear interference model. One or more of the inventive aspects can be applied to one or both of the sliding window and recursive RoT estimation algorithms. Either SIR or power based load factor calculation may be used.
Recall from the discussion regarding HetNets that the surrounding macro cells can interfere with the low power cell to levels such that the UEs of the hotspot are actually connected to the macro cells. To address such issues, in one or more aspects of disclosed subject matter, RNC (radio network controller) or the surrounding RBSs can be informed of the interference situation and can take action as appropriate. For example, admission control in the RNC or functionalities in the surrounding RBSs can be used to reduce the other cell interference and provide better management of the hot spot traffic, e.g., in terms of air interface load. To enable this to take place, the RBS can include capabilities to estimate the other cell interference.
FIG. 4 illustrates an example scenario in which a radio network node 410 (e.g., eNB, eNode B, Node B, base station (BS), radio base station (RBS), and so on) can estimate the other cell interference. In the figure, the radio network node 410 serves one or more wireless terminals 430 (e.g., user equipment, mobile terminal, laptops, M2M (machine-to-machine) terminals, etc.) located within a corresponding cell 420. For clarity, the radio network node 410 will be referred to as an own radio network node, the cell 420 will be referred to as the cell of interest, and the terminals 430 within the cell of interest 420 will be referred to as own terminals. Uplink signaling and data traffic from the own terminals 430 to the own radio network node 410 are illustrated as solid white arrows.
The scenario in FIG. 4 also includes other radio network nodes 415 serving other wireless terminals 435 as indicated by dashed white arrows. When the other terminals 435 transmit to their respective other radio network nodes 415, these signals are also received in the own radio network node 410 as indicated by shaded solid arrows. Such signals act as interferers within the cell of interest 420. A sum of powers of these interfering signals experienced at the own radio network node 410 at time t will be denoted as Pother(t). In other words, the other cell interference Pother(t) may be viewed as expressing a sum of interferences present in the cell of interest due to wireless activities applicable at time t in one or more cells other than in the cell of interest 420. Further, there is a large solid white arrow with no particular source. This represents the thermal noise PN(t) experienced in the own radio network node 410 of the cell of interest 420 at time t.
FIG. 5 illustrates an example embodiment of a radio network node 410. The radio network node 410 may comprise several devices including a controller 510, a transceiver 520, a communicator 530 and a scheduler 540. The transceiver 520 may be structured to wirelessly communicate with wireless terminals 430. The communicator 530 may be structured to communicate with other network nodes and with core network nodes. The controller 510 may be structured to control the overall operations of the radio network node 410.
FIG. 5 provides a logical view of the radio network node. It is not strictly necessary that each device be implemented as physically separate modules or circuits. Some or all devices may be combined in a physical module. Also, one or more devices may be implemented in multiple physical modules as illustrated in FIG. 6.
The devices of the radio network node 410 as illustrated in FIG. 5 need not be implemented strictly in hardware. It is envisioned that any of the devices maybe implemented through a combination of hardware and software. For example, as illustrated in FIG. 6, the radio network node 410 may include one or more central processing units 610 executing program instructions stored in a storage 620 such as non-transitory storage medium or firmware (e.g., ROM, RAM, Flash) to perform the functions of the devices. The radio network node 410 may also include a transceiver 520 structured to receive wireless signals from the wireless terminals 430 and to send signals to the wireless terminals 430 over one or more antennas 525 in one or more channels. The radio network node 410 may further include a network interface 630 to communicate with other network nodes such as the core network nodes.
In one or more aspects, the radio network node 410 can be structured to implement a high performing estimator. The inventive estimator can perform a joint estimation of Pother(t)+PN(t), PN(t), Pother(t) (note the upper case “P”) and the grant utilization probability pgrant(t) (note the lower case “p”). An extended Kalman filter (EKF) can be used in one or more embodiments of the proposed estimator.
The proposed estimator can use any one or more of the following information:

    
    
        Measurements of PRTWP(t), with a sampling rate of TRTWP=kRTWPTTI, kRTWPεZ+. Preferably, the measurements are available for each antenna branch.
        Computed total scheduled grants of the own cell Gown(t), with a sampling rate of TG=kGTTI, kGεZ+. Preferably, scheduled grants are available per cell and are valid on a cell level. They need not necessarily be valid on an antenna branch level with Rx diversity.
        The loop delay TD between the calculation of Gown(t), and the time it takes effect on the air interface. The loop delay may be dependent on the TTI. Preferably, the loop delay is available for and valid per cell.
        Measured total grants of the own cell Gown(t), with a sampling rate of T G=k GTTI, k GεZ+. Preferably, the measured total grants are available per cell, and valid on the cell level. They need not necessarily be valid on the antenna branch level with Rx diversity. The factors can be obtained after TFCI decoding.
    
    


For adaptation to extended Kalman filtering, the following states are modeled:




  
    
      
        
          
        
        ⁢
        
          
            
              
                
                  
                    x
                    
                      1
                      ,
                      1
                    
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
                =
                
                  
                    p
                    grant
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
              
            
            
              
                
              
            
          
          
            
              ⋮
            
            
              
                
                  
                    -
                    grant
                  
                  ⁢
                  
                    
                  
                  ⁢
                  utilization
                  ⁢
                  
                    
                  
                  ⁢
                  probabilities
                
                ,
              
            
          
          
            
              
                
                  
                    x
                    
                      1
                      ,
                      
                        
                          
                            T
                            D
                          
                          /
                          T
                        
                        +
                        1
                      
                    
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
                =
                
                  
                    p
                    grant
                  
                  ⁡
                  
                    (
                    
                      t
                      -
                      
                        T
                        D
                      
                    
                    )
                  
                
              
            
            
              
                
              
            
          
        
      
    
    
      
        (
        12
        )
      
    
  
  
    
      
        
          
            
              
                
                  x
                  2
                
                ⁡
                
                  (
                  t
                  )
                
              
              =
              
                
                  
                    P
                    other
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
                +
                
                  
                    P
                    N
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
              
            
          
          
            
              
                
                  -
                  interference
                
                ⁢
                
                  -
                
                ⁢
                and
                ⁢
                
                  -
                
                ⁢
                noise
                ⁢
                
                  
                
                ⁢
                sum
                ⁢
                
                  
                
                ⁢
                at
                ⁢
                
                  
                
                ⁢
                time
                ⁢
                
                  
                
                ⁢
                t
              
              ,
            
          
        
      
    
    
      
        (
        13
        )
      
    
  




Modeling in one aspect may be viewed as a form of state space modeling where a state space of a physical system is mathematically modeled as a set of input, output and state variables related by equations.

In order to derive a measurement equation for grant utilization, the (C/I) of each user should be related to the load factor of each user. This can be done starting with (7). The idea is that the grant utilization can be modeled by a probability multiplied with the beta factor (e.g., power offset) for the EDPDCH channel for that user, assuming an on-average behavior in terms of grant utilization. This renders (7) as follows:




  
    
      
        
          
            
              
                (
                
                  C
                  /
                  I
                
                )
              
              
                i
                ,
                utilized
              
            
            ⁢
            
              (
              t
              )
            
          
          =
          
            
              
                
                  SINR
                  i
                
                ⁡
                
                  (
                  t
                  )
                
              
              
                W
                i
              
            
            ⁢
            
              RxLoss
              G
            
            ×
            
              (
              
                1
                +
                
                  
                    
                      
                        
                          
                            
                              β
                              
                                DPDCH
                                ,
                                i
                              
                              2
                            
                            ⁡
                            
                              (
                              t
                              )
                            
                          
                          +
                          
                            
                              β
                              
                                EDPCCH
                                ,
                                i
                              
                              2
                            
                            ⁡
                            
                              (
                              t
                              )
                            
                          
                          +
                        
                      
                    
                    
                      
                        
                          
                            
                              p
                              grant
                            
                            ⁡
                            
                              (
                              t
                              )
                            
                          
                          ⁢
                          
                            (
                            
                              
                                
                                  
                                    n
                                    
                                      codes
                                      ,
                                      i
                                    
                                  
                                  ⁡
                                  
                                    (
                                    t
                                    )
                                  
                                
                                ⁢
                                
                                  
                                    β
                                    
                                      EDPDCH
                                      ,
                                      i
                                    
                                    2
                                  
                                  ⁡
                                  
                                    (
                                    t
                                    )
                                  
                                
                              
                              +
                              
                                
                                  β
                                  
                                    HSDPCCH
                                    ,
                                    i
                                  
                                  2
                                
                                ⁡
                                
                                  (
                                  t
                                  )
                                
                              
                            
                            )
                          
                        
                      
                    
                  
                  
                    
                      β
                      DPCCH
                      2
                    
                    ⁡
                    
                      (
                      t
                      )
                    
                  
                
              
              )
            
          
        
        ,
      
    
    
      
        (
        14
        )
      
    
  
  
    
      
        
          
        
        ⁢
        
          
            i
            =
            1
          
          ,
          ...
          ⁢
          
            
          
          ,
          
            I
            .
          
        
      
    
    
      
        
      
    
  




Defining the known time varying quantities




  
    
      
        
          
            
              k
              
                1
                ,
                i
              
            
            ⁡
            
              (
              t
              )
            
          
          =
          
            
              
                
                  SINR
                  i
                
                ⁡
                
                  (
                  t
                  )
                
              
              
                W
                i
              
            
            ⁢
            
              RxLoss
              G
            
            ⁢
            
              (
              
                1
                +
                
                  
                    
                      
                        β
                        
                          DPDCH
                          ,
                          i
                        
                        2
                      
                      ⁡
                      
                        (
                        t
                        )
                      
                    
                    +
                    
                      β
                      
                        EDPCCH
                        ,
                        i
                      
                      2
                    
                  
                  
                    β
                    DPCCH
                    2
                  
                
              
              )
            
          
        
        ,
        
          

        
        ⁢
        
          i
          =
          1
        
        ,
        ...
        ⁢
        
          
        
        ,
        I
      
    
    
      
        (
        15
        )
      
    
  
  
    
      
        
          
            
              k
              
                2
                ,
                i
              
            
            ⁡
            
              (
              t
              )
            
          
          =
          
            
              
                
                  SINR
                  i
                
                ⁡
                
                  (
                  t
                  )
                
              
              
                W
                i
              
            
            ⁢
            
              RxLoss
              G
            
            ⁢
            
              (
              
                
                  
                    
                      n
                      
                        codes
                        ,
                        i
                      
                    
                    ⁢
                    
                      β
                      
                        EDPDCH
                        ,
                        i
                      
                      2
                    
                  
                  +
                  
                    β
                    
                      HSDPCCH
                      ,
                      i
                    
                    2
                  
                
                
                  β
                  DPCCH
                  2
                
              
              )
            
          
        
        ,
        
          

        
        ⁢
        
          i
          =
          1
        
        ,
        ...
        ⁢
        
          
        
        ,
        I
      
    
    
      
        (
        16
        )
      
    
  




transforms (14) to:

(C/I)i,utilized=k1,i(t)+k2,i(t)pgrant(t)i=1, . . . , I.  (17)

In (17), subscript i represents the i'th user in the cell and I represents the total number of users.

Some algebra then transforms (6) to




  
    
      
        
          
            
              
                
                  
                    L
                    i
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
                =
                
                ⁢
                
                  
                    
                      
                        (
                        
                          C
                          /
                          I
                        
                        )
                      
                      i
                    
                    ⁢
                    
                      (
                      t
                      )
                    
                  
                  
                    1
                    +
                    
                      
                        (
                        
                          1
                          -
                          α
                        
                        )
                      
                      ⁢
                      
                        
                          (
                          
                            C
                            /
                            I
                          
                          )
                        
                        i
                      
                      ⁢
                      
                        (
                        t
                        )
                      
                    
                  
                
              
            
          
          
            
              
                
                  =
                  
                  ⁢
                  
                    
                      
                        
                          k
                          
                            1
                            ,
                            i
                          
                        
                        ⁡
                        
                          (
                          t
                          )
                        
                      
                      +
                      
                        
                          
                            k
                            
                              2
                              ,
                              i
                            
                          
                          ⁡
                          
                            (
                            t
                            )
                          
                        
                        ⁢
                        
                          
                            p
                            grant
                          
                          ⁡
                          
                            (
                            t
                            )
                          
                        
                      
                    
                    
                      1
                      +
                      
                        
                          (
                          
                            1
                            -
                            α
                          
                          )
                        
                        ⁢
                        
                          (
                          
                            
                              
                                k
                                
                                  1
                                  ,
                                  i
                                
                              
                              ⁡
                              
                                (
                                t
                                )
                              
                            
                            +
                            
                              
                                
                                  k
                                  
                                    2
                                    ,
                                    i
                                  
                                
                                ⁡
                                
                                  (
                                  t
                                  )
                                
                              
                              ⁢
                              
                                p
                                ⁡
                                
                                  (
                                  t
                                  )
                                
                              
                            
                          
                          )
                        
                      
                    
                  
                
                ,
              
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            i
            =
            1
          
          ,
          ...
          ⁢
          
            
          
          ,
          
            I
            .
          
        
      
    
    
      
        (
        18
        )
      
    
  




Summing up (8), then using (9) and accounting for TD results in




  
    
      
        
          
            P
            RTWP
          
          ⁡
          
            (
            t
            )
          
        
        =
        
          
            
              
                
                  P
                  other
                
                ⁡
                
                  (
                  t
                  )
                
              
              +
              
                
                  P
                  N
                
                ⁡
                
                  (
                  t
                  )
                
              
            
            
              1
              -
              
                
                  ∑
                  
                    i
                    =
                    1
                  
                  I
                
                ⁢
                
                  
                    
                      
                        k
                        
                          1
                          ,
                          i
                        
                      
                      ⁡
                      
                        (
                        
                          t
                          -
                          
                            T
                            D
                          
                        
                        )
                      
                    
                    +
                    
                      
                        
                          k
                          
                            2
                            ,
                            i
                          
                        
                        ⁡
                        
                          (
                          
                            t
                            -
                            
                              T
                              D
                            
                          
                          )
                        
                      
                      ⁢
                      
                        
                          p
                          grant
                        
                        ⁡
                        
                          (
                          
                            t
                            -
                            
                              T
                              D
                            
                          
                          )
                        
                      
                    
                  
                  
                    
                      
                        
                          1
                          +
                          
                            (
                            
                              1
                              -
                              α
                            
                            )
                          
                        
                      
                    
                    
                      
                        
                          (
                          
                            
                              
                                k
                                
                                  1
                                  ,
                                  i
                                
                              
                              ⁡
                              
                                (
                                
                                  t
                                  -
                                  
                                    T
                                    D
                                  
                                
                                )
                              
                            
                            +
                            
                              
                                
                                  k
                                  
                                    2
                                    ,
                                    i
                                  
                                
                                ⁡
                                
                                  (
                                  
                                    t
                                    -
                                    
                                      T
                                      D
                                    
                                  
                                  )
                                
                              
                              ⁢
                              
                                
                                  p
                                  grant
                                
                                ⁡
                                
                                  (
                                  
                                    t
                                    -
                                    
                                      T
                                      D
                                    
                                  
                                  )
                                
                              
                            
                          
                          )
                        
                      
                    
                  
                
              
            
          
          .
        
      
    
    
      
        (
        19
        )
      
    
  




It can be seen that the grant utilization probability pgrant(t) may also be delayed. This can indicate a need of a delay line, i.e., a state augmentation, in the state space filter.
Replacement with selected states and addition of a measurement disturbance then can provide a final measurement model:




  
    
      
        
          
            y
            RTWP
          
          ⁡
          
            (
            t
            )
          
        
        =
        
          
            
              
                x
                2
              
              ⁡
              
                (
                t
                )
              
            
            
              1
              -
              
                
                  ∑
                  
                    i
                    =
                    1
                  
                  I
                
                ⁢
                
                  
                    
                      
                        k
                        
                          1
                          ,
                          i
                        
                      
                      ⁡
                      
                        (
                        
                          t
                          -
                          
                            T
                            D
                          
                        
                        )
                      
                    
                    +
                    
                      
                        
                          k
                          
                            2
                            ,
                            i
                          
                        
                        ⁡
                        
                          (
                          
                            t
                            -
                            
                              T
                              D
                            
                          
                          )
                        
                      
                      ⁢
                      
                        
                          x
                          
                            1
                            ,
                            
                              
                                
                                  T
                                  D
                                
                                /
                                T
                              
                              +
                              1
                            
                          
                        
                        ⁡
                        
                          (
                          t
                          )
                        
                      
                    
                  
                  
                    
                      
                        
                          1
                          +
                          
                            (
                            
                              1
                              -
                              α
                            
                            )
                          
                        
                      
                    
                    
                      
                        
                          (
                          
                            
                              
                                k
                                
                                  1
                                  ,
                                  i
                                
                              
                              ⁡
                              
                                (
                                
                                  t
                                  -
                                  
                                    T
                                    D
                                  
                                
                                )
                              
                            
                            +
                            
                              
                                
                                  k
                                  
                                    2
                                    ,
                                    i
                                  
                                
                                ⁡
                                
                                  (
                                  
                                    t
                                    -
                                    
                                      T
                                      D
                                    
                                  
                                  )
                                
                              
                              ⁢
                              
                                
                                  x
                                  
                                    1
                                    ,
                                    
                                      
                                        
                                          T
                                          D
                                        
                                        /
                                        T
                                      
                                      -
                                      1
                                    
                                  
                                
                                ⁡
                                
                                  (
                                  t
                                  )
                                
                              
                            
                          
                          )
                        
                      
                    
                  
                
              
            
          
          +
          
            
              e
              RTWP
            
            ⁡
            
              (
              t
              )
            
          
        
      
    
    
      
        (
        20
        )
      
    
  
  
    
      
        
          
        
        ⁢
        
          
            
              R
              
                2
                ,
                RTWP
              
            
            ⁡
            
              (
              t
              )
            
          
          =
          
            
              E
              ⁡
              
                [
                
                  
                    e
                    RTWP
                    2
                  
                  ⁡
                  
                    (
                    t
                    )
                  
                
                ]
              
            
            .
          
        
      
    
    
      
        (
        21
        )
      
    
  




In (20) and (21), yRTWP(t)=PRTWP(t) and R2,RTWP(t) denotes the (scalar) covariance matrix of eRTWP(t). The known time varying quantities k1,i(t) and k2,i(t) should be computed and saved to cover the entire delay TD.
Note that (20) represents a nonlinear load curve, expressed in terms of the estimated grant utilization probability x1(t) and the estimated interference-and-noise sum x2(t). That is, (20) can represent a nonlinear curve expressed in terms of {circumflex over (x)}1(t) and {circumflex over (x)}2(t). Equation (20) can be said to relate the momentary combined effect of the estimated quantities and received quantities to the left hand side of the equation, i.e. the momentary measurement of the wideband power. Note that in one or more embodiments, the thermal noise floor N(t) can be used to represent the thermal noise PN(t) and the thermal noise floor estimate {circumflex over (N)}(t) can be used to represent thermal noise estimate {circumflex over (P)}N(t) in these equations.
Measurement of the grant utilization probability pgrant(t) can be made available per cell. As an example, the decoded TFCIs and E-TFCISs show which grants the wireless terminal 430 actually used in the last TTI. This provides the information needed to compute the sum of grants that are actually used, i.e. to compute:




  
    
      
        
          
            
              
                
                  p
                  grant
                
                ⁡
                
                  (
                  t
                  )
                
              
              =
              
              ⁢
              
                
                  
                    
                      G
                      _
                    
                    own
                  
                  ⁡
                  
                    (
                    
                      t
                      -
                      
                        T
                        D
                      
                    
                    )
                  
                
                
                  
                    G
                    own
                  
                  ⁡
                  
                    (
                    
                      t
                      -
                      
                        T
                        D
                      
                    
                    )
                  
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  
                    
                      
                        
                          
                            ∑
                            
                              i
                              =
                              1
                            
                            n
                          
                          ⁢
                          
                            
                              
                                
                                  n
                                  _
                                
                                
                                  codes
                                  ,
                                  i
                                
                              
                              ⁡
                              
                                (
                                
                                  t
                                  -
                                  
                                    T
                                    D
                                  
                                
                                )
                              
                            
                            ⁢
                            
                              
                                
                                  β
                                  _
                                
                                
                                  EDPDCH
                                  ,
                                  i
                                
                                2
                              
                              ⁡
                              
                                (
                                
                                  t
                                  -
                                  
                                    T
                                    T
                                  
                                
                                )
                              
                            
                          
                        
                        +
                      
                    
                  
                  
                    
                      
                        
                          
                            β
                            _
                          
                          
                            HSDPCCH
                            ,
                            i
                          
                          2
                        
                        ⁡
                        
                          (
                          
                            t
                            -
                            
                              T
                              D
                            
                          
                          )
                        
                      
                    
                  
                
                
                  
                    
                      
                        
                          
                            ∑
                            
                              i
                              =
                              1
                            
                            n
                          
                          ⁢
                          
                            
                              
                                n
                                
                                  codes
                                  ,
                                  i
                                
                              
                              ⁡
                              
                                (
                                
                                  t
                                  -
                                  
                                    T
                                    D
                                  
                                
                                )
                              
                            
                            ⁢
                            
                              β
                              
                                EDPDCH
                                ,
                                i
                              
                              2
                            
                            ⁢
                            
                              (
                              
                                t
                                -
                                
                                  T
                                  T
                                
                              
                              )
                            
                          
                        
                        +
                      
                    
                  
                  
                    
                      
                        
                          β
                          
                            HSDPCCH
                            ,
                            i
                          
                          2
                        
                        ⁡
                        
                          (
                          
                            t
                            -
                            
                              T
                              D
                            
                          
                          )
                        
                      
                    
                  
                
              
            
          
        
      
    
    
      
        (
        22
        )
      
    
  




In (22), the quantities with bars are “actual” in the sense that they are reflected by the TFCIs, i.e., they show what the UEs are actually using in their transmissions. Variables without bars denote scheduled quantities, determined by the EUL scheduler. Note that the way the grants are measured is significant. An alternative would be to go for the beta factors linearly. However, the relation (22) reflects the fact that the load is known to vary quadratically with the grants.
After addition of a measurement disturbance, the measurement model for the grant utilization probability measurement becomes:

ygrantUtilization(t)=x1,1(t)+egrantUtilization(t),  (23)

R2,grantUtilization(t)=E[egrantUtilization(t)]2.  (24)

Here ygrantUtilization(t)=pgrant(t) of (22). Furthermore R2,grantUtilization(t) denotes the (scalar) covariance matrix of egrantUtilization(t).
In the dynamic state model, random walk models can be adapted for the state variables x1(t) and x2(t). Hence the following state model can result from the states of (12) and (13).




  
    
      
        
          
            
              
                x
                ⁡
                
                  (
                  
                    t
                    +
                    T
                  
                  )
                
              
              ≡
              
              ⁢
              
                (
                
                  
                    
                      
                        
                          x
                          
                            1
                            ,
                            1
                          
                        
                        ⁡
                        
                          (
                          
                            t
                            +
                            T
                          
                          )
                        
                      
                    
                  
                  
                    
                      ⋮
                    
                  
                  
                    
                      
                        
                          x
                          
                            1
                            ,
                            
                              
                                
                                  T
                                  D
                                
                                /
                                T
                              
                              +
                              1
                            
                          
                        
                        ⁡
                        
                          (
                          
                            t
                            +
                            T
                          
                          )
                        
                      
                    
                  
                  
                    
                      
                        
                          x
                          2
                        
                        ⁡
                        
                          (
                          
                            t
                            +
                            T
                          
                          )
                        
                      
                    
                  
                
                )
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  
                    (
                    
                      
                        
                          1
                        
                        
                          0
                        
                        
                          ...
                        
                        
                          0
                        
                        
                          0
                        
                      
                      
                        
                          1
                        
                        
                          0
                        
                        
                          ...
                        
                        
                          0
                        
                        
                          0
                        
                      
                      
                        
                          0
                        
                        
                          ⋱
                        
                        
                          ⋱
                        
                        
                          
                            
                          
                        
                        
                          ⋱
                        
                      
                      
                        
                          ⋮
                        
                        
                          
                            
                          
                        
                        
                          1
                        
                        
                          0
                        
                        
                          0
                        
                      
                      
                        
                          0
                        
                        
                          0
                        
                        
                          ...
                        
                        
                          0
                        
                        
                          1
                        
                      
                    
                    )
                  
                  ⁢
                  
                    (
                    
                      
                        
                          
                            
                              x
                              
                                1
                                ,
                                1
                              
                            
                            ⁡
                            
                              (
                              t
                              )
                            
                          
                        
                      
                      
                        
                          ⋮
                        
                      
                      
                        
                          
                            
                              x
                              
                                1
                                ,
                                
                                  
                                    
                                      T
                                      D
                                    
                                    /
                                    T
                                  
                                  +
                                  1
                                
                              
                            
                            ⁡
                            
                              (
                              t
                              )
                            
                          
                        
                      
                      
                        
                          
                            
                              x
                              2
                            
                            ⁡
                            
                              (
                              t
                              )
                            
                          
                        
                      
                    
                    )
                  
                
                +
                
                  (
                  
                    
                      
                        
                          
                            w
                            1
                          
                          ⁡
                          
                            (
                            t
                            )
                          
                        
                      
                    
                    
                      
                        0
                      
                    
                    
                      
                        ⋮
                      
                    
                    
                      
                        0
                      
                    
                    
                      
                        
                          
                            w
                            2
                          
                          ⁡
                          
                            (
                            t
                            )
                          
                        
                      
                    
                  
                  )
                
              
            
          
        
      
    
    
      
        (
        25
        )
      
    
  
  
    
      
        
          
            R
            1
          
          ⁡
          
            (
            t
            )
          
        
        =
        
          
            (
            
              
                
                  
                    E
                    ⁡
                    
                      [
                      
                        
                          w
                          1
                          2
                        
                        ⁡
                        
                          (
                          t
                          )
                        
                      
                      ]
                    
                  
                
                
                  0
                
                
                  ...
                
                
                  0
                
                
                  0
                
              
              
                
                  0
                
                
                  0
                
                
                  ...
                
                
                  0
                
                
                  0
                
              
              
                
                  ⋮
                
                
                  
                    
                  
                
                
                  ⋱
                
                
                  
                    
                  
                
                
                  ⋮
                
              
              
                
                  0
                
                
                  
                    
                  
                
                
                  
                    
                  
                
                
                  0
                
                
                  0
                
              
              
                
                  0
                
                
                  0
                
                
                  ...
                
                
                  0
                
                
                  
                    E
                    ⁡
                    
                      [
                      
                        
                          w
                          2
                          2
                        
                        ⁡
                        
                          (
                          t
                          )
                        
                      
                      ]
                    
                  
                
              
            
            )
          
          .
        
      
    
    
      
        (
        26
        )
      
    
  




Preferably, the delay T equals one TTI, but can be any positive integer multiple of the TTI. In (25) and (26), quantities w1(t), . . . , w2(t) represent the so called system noise components, and R1(t) represents the associated covariance matrix.
A state space model behind the EKF can be expressed as follows:

x(t+T)=A(t)x(t)+B(t)u(t)+w(t).  (27)

y(t)=c(x(t))+e(t).  (28)

In (27) and (28), x(t) denotes a state vector, u(t) denotes an input vector (not used in the inventive filtering), y(t) denotes an output measurement vector comprising power measurements performed in a cell (i.e., the total received wideband power PRTWP(t)), w(t) denotes the so called systems noise that represent the model error, and e(t) denotes the measurement error. The matrix A(t) is a system matrix describing the dynamic modes, the matrix B(t) is the input gain matrix, and the vector c(x(t)) is the, possibly nonlinear, measurement vector which is a function of the states of the system. Finally, t represents the time and T represents the sampling period.
The general case with a nonlinear measurement vector is considered here. For this reason, the extended Kalman filter (EKF) should be applied. This filter is given by the following matrix and vector iterations Initialization:




  
    
      
        
          t
          =
          
            t
            0
          
        
        ⁢
        
          

        
        ⁢
        
          
            
              x
              ^
            
            ⁡
            
              (
              
                0
                |
                
                  -
                  1
                
              
              )
            
          
          =
          
            x
            0
          
        
        ⁢
        
          

        
        ⁢
        
          
            P
            ⁡
            
              (
              
                0
                |
                
                  -
                  1
                
              
              )
            
          
          =
          
            P
            0
          
        
        ⁢
        
          

        
        ⁢
        Interation
        ⁢
        
          

        
        ⁢
        
          t
          =
          
            t
            +
            T
          
        
        ⁢
        
          

        
        ⁢
        
          
            C
            ⁡
            
              (
              t
              )
            
          
          =
          
            
              
                
                  ∂
                  
                    c
                    ⁡
                    
                      (
                      x
                      )
                    
                  
                
                
                  ∂
                  x
                
              
              ⁢
              
                |
                
                  x
                  =
                  
                    
                      x
                      ^
                    
                    ⁡
                    
                      (
                      
                        t
                        |
                        
                          t
                          -
                          T
                        
                      
                      )
                    
                  
                
              
              ⁢
              
                

              
              ⁢
              
                
                  K
                  f
                
                ⁡
                
                  (
                  t
                  )
                
              
            
            =
            
              
                P
                ⁡
                
                  (
                  
                    t
                    |
                    
                      t
                      -
                      T
                    
                  
                  )
                
              
              ⁢
              
                
                  C
                  T
                
                ⁡
                
                  (
                  t
                  )
                
              
              ⁢
              
                
                  (
                  
                    
                      
                        C
                        ⁡
                        
                          (
                          t
                          )
                        
                      
                      ⁢
                      
                        P
                        ⁡
                        
                          (
                          
                            t
                            |
                            
                              t
                              -
                              T
                            
                          
                          )
                        
                      
                      ⁢
                      
                        
                          C
                          T
                        
                        ⁡
                        
                          (
                          t
                          )
                        
                      
                    
                    +
                    
                      
                        R
                        2
                      
                      ⁡
                      
                        (
                        t
                        )
                      
                    
                  
                  )
                
                
                  -
                  1
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            
              x
              ^
            
            ⁡
            
              (
              
                t
                |
                t
              
              )
            
          
          =
          
            
              
                x
                ^
              
              ⁡
              
                (
                
                  t
                  |
                  
                    t
                    -
                    T
                  
                
                )
              
            
            +
            
              
                
                  K
                  f
                
                ⁡
                
                  (
                  t
                  )
                
              
              ⁢
              
                (
                
                  
                    y
                    ⁡
                    
                      (
                      t
                      )
                    
                  
                  -
                  
                    c
                    ⁡
                    
                      (
                      
                        
                          x
                          ^
                        
                        ⁡
                        
                          (
                          
                            t
                            |
                            
                              t
                              -
                              T
                            
                          
                          )
                        
                      
                      )
                    
                  
                
                )
              
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            P
            ⁡
            
              (
              
                t
                |
                t
              
              )
            
          
          =
          
            
              P
              ⁡
              
                (
                
                  t
                  |
                  
                    t
                    -
                    T
                  
                
                )
              
            
            -
            
              
                
                  K
                  f
                
                ⁡
                
                  (
                  t
                  )
                
              
              ⁢
              
                C
                ⁡
                
                  (
                  t
                  )
                
              
              ⁢
              
                P
                ⁡
                
                  (
                  
                    t
                    |
                    
                      t
                      -
                      T
                    
                  
                  )
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            
              x
              ^
            
            ⁡
            
              (
              
                
                  t
                  +
                  T
                
                |
                t
              
              )
            
          
          =
          
            
              A
              ⁢
              
                
                  x
                  ^
                
                ⁡
                
                  (
                  
                    t
                    |
                    t
                  
                  )
                
              
            
            +
            
              Bu
              ⁡
              
                (
                t
                )
              
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            P
            ⁡
            
              (
              
                
                  t
                  +
                  T
                
                |
                t
              
              )
            
          
          =
          
            
              
                AP
                ⁡
                
                  (
                  
                    t
                    |
                    t
                  
                  )
                
              
              ⁢
              
                A
                T
              
            
            +
            
              
                
                  R
                  1
                
                ⁡
                
                  (
                  t
                  )
                
              
              .
              
                

              
              ⁢
              End
              .
            
          
        
      
    
    
      
        (
        29
        )
      
    
  




The quantities introduced in the filter iterations (29) are different types of estimates ({circumflex over (x)}(t|t−T), {circumflex over (x)}(t|t), P(t|t−T), and P(t|t)), functions of such estimates (C(t) and Kf(t)), or other quantities (R2(t) and R1(t)), defined as follows:

    
    
        {circumflex over (x)}(t|t−T) denotes a state prediction, based on data up to time t−T,
        {circumflex over (x)}(t|t) denotes a filter update, based on data up to time t,
        P(t|t−T) denotes a covariance matrix of the state prediction, based on data up to time t−T,
        P(t|t) denotes a covariance matrix of the filter update, based on data up to time t,
        C(t) denotes a linearized measurement matrix (linearization around the most current state prediction),
        Kf(t) denotes a time variable Kalman gain matrix,
        R2(t) denotes a measurement covariance matrix, and
        R1(t) denotes a system noise covariance matrix.
    
    


Note that R1(t) and R2(t) are often used as tuning variables of the filter. In principle, the bandwidth of the filter can be controlled by the matrix quotient of R1(t) and R2(t).
An example of an inventive estimation scheme using EKF will be described. The quantities of the EKF for estimation of the other cell interference and the grant utilization can now be defined. Using (19)-(20) and (22)-(25) and (28) it follows that:




  
    
      
        
          
        
        ⁢
        
          
            C
            ⁡
            
              (
              t
              )
            
          
          =
          
            (
            
              
                
                  0
                
                
                  ...
                
                
                  0
                
                
                  
                    
                      C
                      1
                    
                    ⁡
                    
                      (
                      t
                      )
                    
                  
                
                
                  
                    
                      C
                      2
                    
                    ⁡
                    
                      (
                      t
                      )
                    
                  
                
              
              
                
                  1
                
                
                  0
                
                
                  ...
                
                
                  ...
                
                
                  0
                
              
            
            )
          
        
      
    
    
      
        (
        30
        )
      
    
  
  
    
      
        
          
            C
            1
          
          ⁡
          
            (
            t
            )
          
        
        =
        
          
            
              
                
                  x
                  ^
                
                2
              
              ⁡
              
                (
                t
                )
              
            
            ⁢
            
              (
              
                t
                |
                
                  t
                  -
                  T
                
              
              )
            
            ⁢
            
              
                ∑
                
                  i
                  =
                  1
                
                I
              
              ⁢
              
                
                  
                    k
                    
                      2
                      ,
                      i
                    
                  
                  ⁡
                  
                    (
                    
                      t
                      -
                      
                        T
                        D
                      
                    
                    )
                  
                
                
                  
                    (
                    
                      
                        
                          
                            1
                            +
                            
                              (
                              
                                1
                                -
                                α
                              
                              )
                            
                          
                        
                      
                      
                        
                          
                            (
                            
                              
                                
                                  
                                    
                                      
                                        k
                                        
                                          1
                                          ,
                                          i
                                        
                                      
                                      ⁡
                                      
                                        (
                                        
                                          t
                                          -
                                          
                                            T
                                            D
                                          
                                        
                                        )
                                      
                                    
                                    +
                                  
                                
                              
                              
                                
                                  
                                    
                                      
                                        k
                                        
                                          2
                                          ,
                                          i
                                        
                                      
                                      ⁡
                                      
                                        (
                                        
                                          t
                                          -
                                          
                                            T
                                            D
                                          
                                        
                                        )
                                      
                                    
                                    ⁢
                                    
                                      
                                        
                                          x
                                          ^
                                        
                                        
                                          1
                                          ,
                                          
                                            
                                              
                                                T
                                                D
                                              
                                              /
                                              T
                                            
                                            +
                                            1
                                          
                                        
                                      
                                      ⁡
                                      
                                        (
                                        
                                          t
                                          |
                                          
                                            t
                                            -
                                            T
                                          
                                        
                                        )
                                      
                                    
                                  
                                
                              
                            
                            )
                          
                        
                      
                    
                    )
                  
                  2
                
              
            
          
          
            
              (
              
                1
                -
                
                  
                    ∑
                    
                      i
                      =
                      1
                    
                    I
                  
                  ⁢
                  
                    
                      
                        
                          
                            
                              
                                k
                                
                                  1
                                  ,
                                  i
                                
                              
                              ⁡
                              
                                (
                                
                                  t
                                  -
                                  
                                    T
                                    D
                                  
                                
                                )
                              
                            
                            +
                          
                        
                      
                      
                        
                          
                            
                              
                                k
                                
                                  2
                                  ,
                                  i
                                
                              
                              ⁡
                              
                                (
                                
                                  t
                                  -
                                  
                                    T
                                    D
                                  
                                
                                )
                              
                            
                            ⁢
                            
                              
                                
                                  x
                                  ^
                                
                                
                                  1
                                  ,
                                  
                                    
                                      
                                        T
                                        D
                                      
                                      /
                                      T
                                    
                                    +
                                    1
                                  
                                
                              
                              ⁡
                              
                                (
                                
                                  t
                                  |
                                  
                                    t
                                    -
                                    T
                                  
                                
                                )
                              
                            
                          
                        
                      
                    
                    
                      
                        
                          
                            1
                            +
                            
                              (
                              
                                1
                                -
                                α
                              
                              )
                            
                          
                        
                      
                      
                        
                          
                            (
                            
                              
                                
                                  
                                    
                                      
                                        k
                                        
                                          1
                                          ,
                                          i
                                        
                                      
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        (
        37
        )
      
    
  




In order to execute the EKF, the state prediction and the state covariance prediction at time t are needed, they are given by the following equations:




  
    
      
        
          
        
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          .
        
      
    
    
      
        (
        39
        )
      
    
  




The equations (30)-(39) define the EKF completely, when inserted in (29). The final step to compute the other cell interference estimate can be:

{circumflex over (P)}other(t|t)={circumflex over (x)}2(t|t)−{circumflex over (P)}N(t|t).  (40)

FIG. 7 illustrates a flow chart of example method 700 performed by a radio network node 410 to implement a high performing estimator. The method 700 may be performed by the scheduler 540, e.g., as grant utilization estimation functionality associated with the scheduler 540, to determine the other cell interference Pother(t). In particular, the other cell interference estimate Pother(t) can be determined. The other cell interference Pother(t) can express a sum of interferences present in the cell of interest 420 due to wireless activities applicable at the time t in one or more cells other than in the cell of interest.
As illustrated, in step 710, the radio network node 410, and in particular the scheduler 540, can estimate the grant utilization probability pgrant(t1) to obtain a grant utilization probability estimate {circumflex over (p)}grant(t1) applicable at a time t=t1. The estimation can be made based on at least on a grant utilization probability estimate {circumflex over (p)}grant(t) and an interference-and-noise sum estimate {circumflex over (P)}other(t0))+{circumflex over (P)}N(t0) applicable at time t=t0. It should be noted that the term “t” enclosed in parentheses in the expressions without subscripts (e.g., Pother(t), pload(t), etc.) is intended to indicate time variable in general, and the same term “t” enclosed in parentheses with subscripts (e.g., Pother(t0), pload(t1) etc.) is intended to indicate a particular time. Thus, time t1 may also be viewed as t=t1 for example.
The particular times t0 and t1 are assumed such that t1−t0=T>0. T can represent a duration between estimation times. In an embodiment, T is a positive integer multiple of a transmission time interval, preferably one (e.g., for 10 ms TTI) but can be larger (e.g., 5 for 2 ms TTI). In the method 700, it can be assumed the values of the quantities at time t=t0 (or simply at time t0) are known (have been measured, computed, received, or otherwise have been determined), and the values of one or more quantities at time t=t1 are estimated or otherwise predicted.
In step 720, the radio network node 410 can estimate the interference-and-noise sum Pother(t1)+PN(t1) to obtain the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) applicable at the time t=t1. This estimation can be made based at least on the grant utilization probability estimate {circumflex over (p)}grant(t0) and the interference-and-noise sum estimate {circumflex over (P)}other(t0)+{circumflex over (P)}N(t0)
FIG. 8 illustrates a flow chart of an example process performed by the radio network node 410 to implement the steps 710 and 720 to obtain the grant utilization probability estimate {circumflex over (p)}grant(t1) and to obtain the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1). In step 810, a total scheduled grant Gown(t1−TD) can be calculated. Here, TD can represent a delay between the calculation of the total scheduled grant and a time the schedule takes effect on an air interface. The total scheduled grant Gown(t−TD) can express an amount of the radio resources granted for use by the cell terminals 430 for uplink transmissions at the time t.
In step 820, a total used grant Gown(t1−TD) can be obtained. Note that the total used grant Gown(t−TD) can express an amount of the radio resource grants used by the cell terminals 430 for the uplink transmissions at the time t.
In step 830, a grant utilization




  
    
      
        G
        _
      
      own
    
    ⁡
    
      (
      
        
          t
          1
        
        -
        
          T
          D
        
      
      )
    
  
  
    
      G
      own
    
    ⁡
    
      (
      
        
          t
          1
        
        -
        
          T
          D
        
      
      )
    
  




can be measured or otherwise determined. Based on the measured grant utilization





  
    
      y
      grantUtilization
    
    =
    
      
        
          
            G
            _
          
          own
        
        ⁡
        
          (
          
            
              t
              1
            
            -
            
              T
              D
            
          
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          own
        
        ⁡
        
          (
          
            
              t
              1
            
            -
            
              T
              D
            
          
          )
        
      
    
  
  ,




the grant utilization probability estimate {circumflex over (p)}grant(t1) can be obtained in step 840 and the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) can be obtained in step 850.

FIG. 9 illustrates a flow chart of another example process performed by the radio network node 410 to implement the steps 710 and 720 to obtain the grant utilization probability estimate {circumflex over (p)}grant(t1) and to obtain the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1). In step 910, a total wideband power yRTWP(t1) can be measured. Based on the measured total wideband power yRTWP(t1), the grant utilization probability estimate {circumflex over (p)}grant(t1) can be obtained in step 920, and the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) can be obtained in step 930.
FIG. 10 illustrates a flow chart of an example process performed by the radio network node 410 to implement the step 930 to obtain the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1). In step 1010, a gain factor g(t1) can be determined based on the grant utilization probability estimate {circumflex over (p)}grant(t1) and the total scheduled grant Gown(t0). In step 1020, the measured total wideband power yRTWP(t1) can be modeled as a combination of the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) weighted by the gain factor g(t1) and a measurement uncertainty eRTWP(t1). Based on the measured total wideband power yRTWP(t1) and the modeling thereof, the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) can be obtained.
Referring back to FIG. 7, once the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) is determined in step 720, the radio network node 410 can estimate the other cell interference Pother(t1), i.e., obtain the other cell interference estimate {circumflex over (P)}other(t1). The estimation can be based at least on the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) and a thermal noise estimate {circumflex over (P)}N(t1). Note that the interference-and-noise sum Pother(t)+PN(t) can express a sum of undesired signals, other than an own cell load Pown(t). In FIG. 4, the interference-and-noise sum Pother(t)+PN(t) are visually illustrated with shaded arrows (from the other terminals 435) and the large white arrow.
It can then be seen that once the once the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) is determined, the other cell interference estimate {circumflex over (P)}other(t) can be arrived at if the thermal noise {circumflex over (P)}N(t) can be determined. FIG. 11 illustrates a flow chart of an example process performed by the radio network node 410 to implement the step 730 of estimating the other cell interference Pother(t1). In step 1110, the thermal noise estimate {circumflex over (P)}N(t1) can be obtained. In one embodiment, a thermal noise floor estimate {circumflex over (N)}(t1) corresponding to the cell of interest 1120 can be obtained as the thermal noise estimate {circumflex over (P)}N(t1). In step 1120, thermal noise estimate {circumflex over (P)}N(t1) can be subtracted from the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) to obtain the other cell interference estimate {circumflex over (P)}other(t1).
FIG. 12 illustrates another flow chart of an example process performed by the radio network node 410 to implement the steps 710 and 720 to obtain the grant utilization probability estimate pgrant(t1) and to obtain the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1). FIG. 12 may be viewed as a specific instance of the flow chart illustrated in FIG. 8. In FIG. 12, the extended Kalman filtering adapted for estimation is used.
In step 1210, the grant utilization probabilities pgrant(t) and the interference-and-noise sum Pother(t)+PN(t) can be modeled as states x1,1(t)=pgrant(t)′, . . . , x1,TD/T+1(t)=pgrant(t−T), x2(t)=Pother(t)+PN(t) in a state vector x(t) of a state space model. The state x1,TD/TTTI+1(t)=pgrant(t−T) may reflect that the grant utilization probability may be subject to a delay corresponding to the sampling period T.
In this context, the state space model can be characterized through equations x(t+T)=A(t)x(t)+B(t)u(t)+w(t) and y(t)=c(x(t))+e(t). In these equations, x(t) represents the state vector, u(t) represents an input vector, y(t) represents the output measurement vector, w(t) represents a model error vector, e(t) represents a measurement error vector, A(t) represents a system matrix describing dynamic modes of the system, B(t) represents an input gain matrix, c(x(t)) represents a measurement vector which is a function of the states of the system, t represents the time and T represents a sampling period. Thus, it is seen that modeling errors and measurement errors are incorporated in the state space model.
In step 1220, the measured total wideband power yRTWP(t) and the measured grant utilization ygrantUtilization(t) can be modeled in the output measurement vector y(t) of the state space model.
In step 1230, a predicted state vector {circumflex over (x)}(t1|t0) can be obtained. The predicted state vector {circumflex over (x)}(t1|t0) includes predicted states {circumflex over (x)}1,1(t1|t0), {circumflex over (x)}1,2(t1|t0) . . . {circumflex over (x)}1,I(t), {circumflex over (x)}1,TD/TTTI+1(t1|t0) and {circumflex over (x)}2(t1|t0) whose values are based on the grant utilization probability estimate {circumflex over (p)}grant(t0) and the interference-and-noise sum estimate {circumflex over (P)}other(t0)+{circumflex over (P)}N(t0). In this context, the predicted state vector {circumflex over (x)}(t|t−T) denotes a prediction of the state vector x(t) based on information available up to time t−T. Recall from above that t1−t0=T>0. Thus, the predicted state vector {circumflex over (x)}(t1|t0) denotes a prediction the state vector x(t) at time t=t1 based on information available up to time t=t0. The time t=t0 can be a time of initialization or a time of a previous iteration.
In step 1240, the predicted state vector {circumflex over (x)}(t1|t0) can be updated based on one or more measurements included in an output measurement vector y(t1) applicable at the time t=t1 to obtain an estimated state vector {circumflex over (x)}(t1|t1)={circumflex over (x)}(t1). The measurements can include the measured received total wideband power yRTWP(t1) and the grant utilization ygrantUtilization(t1). The solid white arrow entering the step 1240 in FIG. 12 is to indicate that measurements may come into the step. Generally, the estimated state vector {circumflex over (x)}(t|t)={circumflex over (x)}(t) denotes an estimate of the state vector x(t) based on information available up to time t. This step corresponds to an adjusting step of the (extended) Kalman filter algorithm in which the prediction made in the previous time (e.g., at time t=t0) is adjusted according to measurements made in the current time (e.g., at time t=t1).
In step 1250, the estimated states {circumflex over (x)}1,1(t1), {circumflex over (x)}1,2(t1) . . . {circumflex over (x)}1,I(t1) can be obtained from the estimated state vector {circumflex over (x)}(t1) respectively as the grant utilization probability estimates of the delay line chain, {circumflex over (x)}1,1(t1)={circumflex over (p)}grant(t1), . . . , {circumflex over (x)}1,TD/T+1(t1)={circumflex over (p)}grant(t1−TD) Also from the estimated state vector {circumflex over (x)}(t1), estimated state {circumflex over (x)}2(t1)={circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) may be obtained.
In step 1260, the estimated state vector {circumflex over (x)}(t1) may be projected based at least on dynamic modes corresponding to the cell of interest to obtain a predicted state vector {circumflex over (x)}(t2|t1), t2−t1=T. Here, the predicted state vector {circumflex over (x)}(t2|t1) includes predicted states {circumflex over (x)}1,1(t2|t1), {circumflex over (x)}1,2(t2|t1) . . . {circumflex over (x)}1,I(t1|t1), and {circumflex over (x)}2(t2|t1) whose values are based on the grant utilization probability estimate {circumflex over (p)}grant(t1) and the interference-and-noise sum estimate {circumflex over (x)}2(t1)={circumflex over (P)}other(t1)+{circumflex over (P)}N(t1). This step corresponds to a predicting step of the Kalman filter algorithm in which future states are predicted based on current information. As seen, the steps in FIG. 12 can be iteratively performed.
In one embodiment, the steps 1240 and 1260 of updating the predicted state vector {circumflex over (x)}(t1|t0) and of projecting the estimated state vector {circumflex over (x)}(t1|t1) comprise performing a Kalman filter process to iteratively predict and update the state vector x(t) to obtain the estimated state vector {circumflex over (x)}(t). Here, the estimated state vector {circumflex over (x)}(t) includes the estimated states {circumflex over (x)}1,1(t), {circumflex over (x)}1,2(t) . . . {circumflex over (x)}1,I(t) and {circumflex over (x)}2(t) which may correspond to grant utilization probability estimates {circumflex over (p)}grant(t1) of the delay line chain and the interference-and-noise sum estimate {circumflex over (x)}2(t1)={circumflex over (P)}other(t1)+{circumflex over (P)}N(t1).
FIG. 13 illustrates a flow chart of an example process performed by the radio network node 410 to implement the step 1240 to update predicted state vector {circumflex over (x)}(t1|t0). Here, it is assumed that the state x1,TD/TTTI+1(t) is also modeled in the state vector {circumflex over (x)}(t). In step 1310, the measured total wideband power yRTWP(t1) applicable at the time t=t1 can be modeled as:




  
    
      
        
          
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Here, TD can represent a delay between calculation of the schedule and a time the schedule takes effect on an air interface. Also, eRTWP(t) can represent a measurement error.

In step 1320, the grant utilization ygrantUtilization(t1) applicable at the time t=t1 as can be modeled as:

ygrantUtilization(t)=x1,1(t)+egrantUtilization(t).  (42)

Again, egrantUtilization(t) can represent a measurement error.

In step 1330, a measurement matrix C(t1) around the predicted state vector {circumflex over (x)}(t1|t0) can be obtained. Here, the predicted state vector {circumflex over (x)}(t1|t0) can include the predicted states {circumflex over (x)}1,1(t1|t0), {circumflex over (x)}1,2(t1|t0) . . . {circumflex over (x)}1,I(t1|t0), {circumflex over (x)}1,TD/TTTI+1(t1|t0) and {circumflex over (x)}2(t1|t0) which are predicted based on data up to the time t=t0. In an embodiment, the measurement matrix C(t1) can be obtained by determining the measurement matrix C(t1) linearized around the predicted state vector {circumflex over (x)}(t1|t0) such that




  
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In step 1340, a Kalman gain matrix Kf(t1) can be obtained based on at least the measurement matrix C(t1), the measurement error vector e(t1), and a predicted covariance matrix P(t1|t0) corresponding to the predicted state vector {circumflex over (x)}(t1|t0). In an embodiment, the Kalman gain matrix Kf(t1) can be obtained by determining:

Kf(t1)=P(t1|t0)CT(t1)(C(t1)P(t1|t0)CT(t1)+R2(t1))−1  (43)

in which CT(t) is a transpose of the measurement matrix C(t) and (R2(t)) is a measurement covariance matrix corresponding to the measurement error vector e(t).

In step 1350, the predicted state vector {circumflex over (x)}(t1|t0) can be updated based on at least the Kalman gain matrix Kf(t1), the output measurement vector y(t1), and the measurement vector c(x(t1)) to obtain the estimated state vector {circumflex over (x)}(t1|t1)={circumflex over (x)}(t1). The estimated state vector {circumflex over (x)}(t1) can include the estimated states {circumflex over (x)}1,1(t1), {circumflex over (x)}1,2(t1) . . . {circumflex over (x)}1,I(t1), {circumflex over (x)}1,TD/TTTI+1(t1) and {circumflex over (x)}2(t1). In an embodiment, the estimated state vector {circumflex over (x)}(t1|t1)={circumflex over (x)}(t1) can be obtained through determining:

{circumflex over (x)}(t1|t1)={circumflex over (x)}(t1|t0)+Kf(t1)(y(t1)−c({circumflex over (x)}(t1|t0))).  (45)

Here y(t1) is the measurement vector, with components being the received total wideband power measurement and the grant utilization measurement.

In step 1360, the predicted covariance matrix P(t1|t0) can be updated based on at least the Kalman gain matrix Kf(t1) and the measurement matrix C(t1) to obtain an updated covariance matrix P(t1|t1) corresponding to the estimated state vector {circumflex over (x)}(t1). In an embodiment, the updated covariance matrix P(t1|t1) can be obtained through determining:

P(t1|t1)=P(t1|t0)−Kf(t1)C(t1)P(t1|t0).  (46)

Referring back to FIG. 12, the step 1260 of projecting the estimated state vector {circumflex over (x)}(t1) can comprise projecting the estimated state vector {circumflex over (x)}(t1) based on at least the system matrix A(t1) to obtain the predicted state vector {circumflex over (x)}(t2|t1). Here, the predicted state vector {circumflex over (x)}(t2|t1) includes the predicted states {circumflex over (x)}1,1(t2|t1), {circumflex over (x)}1,2(t2|t1) . . . {circumflex over (x)}1,I(t2|t1), {circumflex over (x)}1,TD/TTTI+1(t2|t1) and {circumflex over (x)}1(t2|t1). Then in step 1270, the updated covariance matrix P(t1|t1) can be projected to obtain a predicted covariance matrix P(t2|t1) based on at least the system matrix A(t1) and a system noise covariance matrix R1(t1). Back in step 1260, the predicted state vector {circumflex over (x)}(t2|t1) can be obtained by determining {circumflex over (x)}(t2|t1)=A{circumflex over (x)}(t1|t1)+Bu(t1), and in step 1270, the predicted covariance matrix P(t2|t1) can be obtained through determining P(t2|t1)=AP(t1|t1)AT+R1(t1) in which AT is a transpose of the system matrix A(t). Note that the input gain matrix B(t) can be set to zero.
There are several advantages of the disclosed subject matter. Among them is in enhancing the performance of the whole mobile broadband cellular system, e.g., WCDMA RAN. This can lead to (among others):
Enhanced interference management in HetNets;
Corresponding enhanced system capacity.
Although the description above contains many specificities, these should not be construed as limiting the scope of the disclosed subject matter but as merely providing illustrations of some of the presently preferred embodiments. Therefore, it will be appreciated that the scope of the disclosed subject matter fully encompasses other embodiments, and that the scope is accordingly not to be limited. All structural, and functional equivalents to the elements of the above-described preferred embodiment that are known to those of ordinary skill in the art are expressly incorporated herein by reference and are intended to be encompassed hereby. Moreover, it is not necessary for a device or method to address each and every problem described herein or sought to be solved by the present technology, for it to be encompassed hereby.

## Claims

1. A method (700) performed at a radio network node (410) corresponding to a cell of interest (420) in a wireless network (400), the radio network node comprising a processor configured to execute instructions store in memory, the method (700) comprising:
estimating (710), by the processor, a grant utilization probability pgrant(t1) based at least on a grant utilization probability estimate {circumflex over (p)}grant(t0) and an interference-and-noise sum estimate {circumflex over (P)}other(t0)+{circumflex over (P)}N(t0) applicable at a time t0 to obtain a grant utilization probability estimate {circumflex over (p)}grant(t1) applicable at a time t1, wherein t1−t0=T>0;
estimating (720), by the processor, an interference-and-noise sum Pother(t1)+PN(t1) based at least on the grant utilization probability estimate {circumflex over (p)}grant(t1) and the interference-and-noise sum estimate {circumflex over (P)}other(t0)+{circumflex over (P)}N(t0) to obtain an interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) applicable at the time t1; and
estimating (730), by the processor, an other cell interference Pother(t1) based at least on the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) and a thermal noise estimate {circumflex over (P)}N(t1) to obtain an other cell interference estimate {circumflex over (P)}other(t1) applicable at the time t1,
wherein the grant utilization probability pgrant(t) expresses a relationships between radio resource grants scheduled to one or more cell terminals and radio resource grants used by the same cell terminals applicable at a time t, each cell terminal being a wireless terminal in the cell of interest, and the grant utilization probability estimate {circumflex over (p)}grant(t) being an estimate thereof,
wherein the interference-and-noise sum Pother(t)+PN(t) expresses a sum of undesired signals, other than an own cell load Pown(t), applicable at the time t, and the interference-and-noise sum estimate {circumflex over (P)}other(t)+{circumflex over (P)}N(t) being an estimate thereof,
wherein the own cell load Pown(t) expresses a sum of signals due to wireless activities in the cell of interest applicable at the time t,
wherein the other cell interference Pother(t) expresses a sum of interferences present in the cell of interest due to wireless activities applicable at the time t in one or more cells other than in the cell of interest, and the other cell interference estimate {circumflex over (P)}other(t) being an estimate thereof, and
wherein a thermal noise PN(t) expresses a sum of undesired signals present in the cell of interest at the time t other than the own cell load Pown(t) and other than the other cell interference Pother(t), and the thermal noise estimate {circumflex over (P)}N(t) being an estimate thereof.

2. The method of claim 1, wherein estimating, by the processor, the grant utilization probability pload(t1) and estimating the interference-and-noise sum Pother(t1)+PN(t1) comprise:
calculating a total scheduled grant Gown(t1−TD);
obtaining a total used grant Gown(t1−TD);
measuring a grant utilization





  
    
      
        
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obtaining the grant utilization probability estimate {circumflex over (p)}grant(t1) based on the measured grant utilization





  
    
      
        
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and
obtaining the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) based on the measured grant utilization





  
    
      
        
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wherein the total scheduled grant Gown(t−TD) expresses an amount of the radio resources granted for use by the cell terminals for uplink transmissions at the time t, and
wherein the total used grant Gown(t1−TD) expresses an amount of the radio resource grants used by the cell terminals for the uplink transmissions at the time t, and
wherein TD represents a delay between calculation of the total scheduled grant and a time the schedule takes effect on an air interface.

3. The method of claim 1, wherein estimating, by the processor, the grant utilization probability pgrant(t1) and estimating the interference-and-noise sum Pother(t1)+PN(t1) comprise:
measuring a total wideband power yRTWP(t1):
obtaining the grant utilization probability estimate {circumflex over (p)}grant(t1) based on the measured total wideband power yRTWP(t1); and
obtaining the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) based on the measured total wideband power yRTWP(t1).

4. The method of claim 3, wherein obtaining the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) comprises:
determining a gain factor g(t1) based on the grant utilization probability estimate {circumflex over (p)}load(t1) and the total scheduled grant Gown(t0);
modeling the measured total wideband power yRTWP(t1) as a combination of the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) weighted by the gain factor g(t1) and a measurement uncertainty eRTWP(t1); and
obtaining the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) based on the measured total wideband power yRTWP(t1) and the model thereof.

5. The method of claim 1, wherein estimating, by the processor, the grant utilization probability pgrant(t1) and estimating the interference-and-noise sum Pother(t1)+PN(t1) comprise:
modeling the grant utilization probability pgrant(t) and the interference-and-noise sum Pother(t)+PN(t) as states




  
    
      
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and x2(t)=Pother(t)+PN(t) in a state vector x(t) of a state space model;
modeling a measured total wideband power yRTWP(t) and a measured grant utilization ygrantUtilization(t) in an output measurement vector y(t) of the state space model;
obtaining a predicted state vector {circumflex over (x)}(t1|t0) which includes therein predicted states {circumflex over (x)}1,1(t1|t0), {circumflex over (x)}1,2(t1|t0) . . . {circumflex over (x)}1,I(t1|t0), {circumflex over (x)}1,TD/TTTI+1(t1|t0), {circumflex over (x)}2(t1|t0) whose values are based on the grant utilization probability estimate {circumflex over (p)}grant(t0) and the interference-and-noise sum estimate {circumflex over (P)}other(t0)+{circumflex over (P)}N(t0);
updating the predicted state vector {circumflex over (x)}(t1|t0) based on one or more measurements included in an output measurement vector y(t1) applicable at the time t1 to obtain an estimated state vector {circumflex over (x)}(t1|t1)={circumflex over (x)}(t1); and
obtaining estimated states {circumflex over (x)}1,1(t1), {circumflex over (x)}1,2(t1) . . . {circumflex over (x)}1,I(t1), {circumflex over (x)}2(t1) from the estimated state vector {circumflex over (x)}(t1) as the grant utilization probability estimate of the delay line chain {circumflex over (x)}1,1(t1)={circumflex over (p)}grant(t1), . . . , {circumflex over (x)}1,TD/T+1(t1)={circumflex over (p)}grant(t1−tD), and the interference-and-noise sum estimate {circumflex over (x)}2(t1)={circumflex over (P)}other(t1)+{circumflex over (P)}N(t1),
wherein modeling errors and measurement errors are incorporated in the state space model as a model error vector w(t) and a measurement error vector e(t),
wherein the predicted state vector {circumflex over (x)}(t|t−T) denotes a prediction of the state vector x(t) based on information available up to a time t−T, and
wherein the estimated state vector {circumflex over (x)}(t|t)={circumflex over (x)}(t) denotes an estimate of the state vector x(t) based on information available up to the time t.

6. The method of claim 5, wherein updating the predicted state vector {circumflex over (x)}(t1|t0) comprises:
modeling the measured total wideband power yRTWP(t1) applicable at the time t1 as





  
    
      
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TD representing a delay between calculation of the schedule and a time the schedule takes effect on an air interface;
modeling the grant utilization ygrantUtilization(t1) applicable at the time t1 as ygrantUtilization(t1)=x1,1(t1)+egrantUtilization(t1);
obtaining a measurement matrix C(t1) around the predicted state vector {circumflex over (x)}(t1|t0), the predicted state vector {circumflex over (x)}(t1|t0) including the predicted states predicted states {circumflex over (x)}1,1(t1|t0), {circumflex over (x)}1,2(t1|t0) . . . {circumflex over (x)}1,I(t1|t0), {circumflex over (x)}1,TD/TTTI+1(t1|t0) and {circumflex over (x)}2(t1|t0) predicted based on data up to the time t0;
obtaining a Kalman gain matrix Kf(t1) based on at least the measurement matrix C(t1), the measurement error vector e(t1), and a predicted covariance matrix P(t1|t0) corresponding to the predicted state vector {circumflex over (x)}(t1|t0);
updating the predicted state vector {circumflex over (x)}(t1|t0) based on at least the Kalman gain matrix Kf(t1), the output measurement vector y(t1), and the measurement vector c(x(t1)) to obtain the estimated state vector {circumflex over (x)}(t1|t1)={circumflex over (x)}(t1), the estimated state vector {circumflex over (x)}(t1) including the estimated states {circumflex over (x)}1,1(t1), {circumflex over (x)}1,2(t1) . . . {circumflex over (x)}1,I(t1), {circumflex over (x)}1,TD/TTTI+1(t1) and {circumflex over (x)}2(t1); and
updating the predicted covariance matrix P(t1|t0) based on at least the Kalman gain matrix Kf(t1) and the measurement matrix C(t1) to obtain an updated covariance matrix P(t1|t1) corresponding to the estimated state vector {circumflex over (x)}(t1).

7. The method of claim 6,
wherein obtaining the measurement matrix C(t1) comprises determining the measurement matrix C(t1) linearized around the predicted state vector {circumflex over (x)}(t1|t0) such that





  
    
      C
      ⁡
      
        (
        t
        )
      
    
    =
    
      
        
          ∂
          
            c
            ⁡
            
              (
              x
              )
            
          
        
        
          ∂
          x
        
      
      ⁢
      
        |
        
          x
          =
          
            
              x
              ^
            
            ⁡
            
              (
              
                
                  t
                  ⁢
                  
                    
                  
                  ⁢
                  1
                
                |
                
                  t
                  ⁢
                  
                    
                  
                  ⁢
                  0
                
              
              )
            
          
        
      
    
  
  ,



wherein obtaining the Kalman gain matrix Kf(t1) comprises determining Kf(t1)=P(t1|t0)CT(t1)(C(t1)P(t1|t0)CT(t1)+R2(t1))−1 in which CT(t) is a transpose of the measurement matrix C(t) and (R2(t)) is a measurement covariance matrix corresponding to the measurement error vector e(t),
wherein updating the predicted state vector {circumflex over (x)}(t1|t0) to obtain the estimated state vector {circumflex over (x)}(t1|t1)={circumflex over (x)}(t1) comprises determining {circumflex over (x)}(t1|t1)={circumflex over (x)}(t1|t0)+Kf(t1)(y(t1)−c({circumflex over (x)}(t1|t0))), and
wherein updating the predicted covariance matrix P(t1|t0) to obtain the updated covariance matrix P(t1|t1) comprises determining P(t1|t1)=P(t1|t0)−Kf(t1)C(t1)P(t1|t0).

8. The method of claim 5, further comprising:
projecting, by the processor, the estimated state vector {circumflex over (x)}(t1) based at least on dynamic modes corresponding to the cell of interest to obtain a predicted state vector {circumflex over (x)}(t2|t1), t2−t1=T,
wherein the predicted state vector {circumflex over (x)}(t2|t1) includes predicted states {circumflex over (x)}1,1(t2|t1), {circumflex over (x)}1,2(t2|t1) . . . {circumflex over (x)}1,I(t2|t1), {circumflex over (x)}1,TD/TTTI+1(t2|t1) and {circumflex over (x)}2(t2|t1), and
wherein the state space model is characterized through equations x(t+T)=A(t)x(t)+B(t)u(t)+w(t) and y(t)=c(x(t))+e(t), in which x(t) represents the state vector, u(t) represents an input vector, y(t) represents the output measurement vector, w(t) represents the model error vector, e(t) represents the measurement error vector, A(t) represents a system matrix describing dynamic modes of the system, B(t) represents an input gain matrix, c(x(t)) represents a measurement vector which is a function of the states of the system, t represents the time and T represents a sampling period.

9. The method of claim 6, wherein the method further comprises projecting, by the processor, the updated covariance matrix P(t1|t1) to obtain a predicted covariance matrix P(t2|t1) based on at least the system matrix A(t1) and a system noise covariance matrix R1(t1).

10. The method of claim 9,
wherein projecting the estimated state vector {circumflex over (x)}(t1) to obtain the predicted state vector {circumflex over (x)}(t2|t1) comprises determining {circumflex over (x)}(t2|t1)=A{circumflex over (x)}(t1|t1)+Bu(t1), and
wherein projecting the updated covariance matrix P(t1|t1) to obtain the predicted covariance matrix P(t2|t1) comprises determining P(t2|t1)=AP(t1|t1)AT+R1(t1) in which AT is a transpose of the system matrix A(t).

11. The method of claim 1, wherein estimating the other cell interference Pother(t1) comprises:
obtaining a thermal noise floor estimate {circumflex over (N)}(t1) corresponding to the cell of interest as the thermal noise estimate {circumflex over (P)}N(t1); and
subtracting the thermal noise estimate {circumflex over (P)}N(t1) from the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) to obtain the other cell interference estimate {circumflex over (P)}other(t1).

12. The method of claim 1, wherein T is equal to a transmission time interval (TTI).

13. A radio network node of a wireless network, the radio network node corresponding to a cell of interest and being structured to determine an other cell interference Pother(t) the radio network node comprising:
a transceiver structured to transmit and receive wireless signals via one or more antennas from and to one or more cell terminals located within the cell of interest;
a communicator structured to communicate with other network nodes; and
a scheduler structured to schedule uplink transmissions from the cell terminals,
wherein the scheduler is structured to:
estimate a grant utilization probability pgrant(t1) based at least on a grant utilization probability estimate {circumflex over (p)}grant(t0) and an interference-and-noise sum estimate {circumflex over (P)}other(t0)+{circumflex over (P)}N(t0) applicable at a time t0 to obtain a grant utilization probability estimate {circumflex over (p)}grant(t1) applicable at a time t1, wherein t1−t0=T>0,
estimate an interference-and-noise sum Pother(t1)+PN(t1) based at least on the grant utilization probability estimate {circumflex over (p)}grant(t1) and the interference-and-noise sum estimate {circumflex over (P)}other(t0)+{circumflex over (P)}N(t0) to obtain an interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) applicable at the time t1, and
estimate an other cell interference Pother(t1) based at least on the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) and a thermal noise estimate {circumflex over (P)}N(t1) to obtain an other cell interference estimate {circumflex over (P)}other(t1) applicable at the time t1,

wherein the grant utilization probability pgrant(t) expresses a relationships between radio resource grants scheduled to one or more cell terminals and radio resource grants used by the same cell terminals applicable at a time t, each cell terminal being a wireless terminal in the cell of interest, and the grant utilization probability estimate {circumflex over (p)}grant(t) being an estimate thereof,
wherein the interference-and-noise sum Pother(t)+PN(t) expresses a sum of undesired signals, other than an own cell load Pown(t), applicable at the time t, and the interference-and-noise sum estimate {circumflex over (P)}other(t)+{circumflex over (P)}N(t) being an estimate thereof,
wherein the own cell load Pown(t) expresses a sum of signals due to wireless activities in the cell of interest applicable at the time t,
wherein the other cell interference Pother(t) expresses a sum of interferences present in the cell of interest due to wireless activities applicable at the time t in one or more cells other than in the cell of interest, and the other cell interference estimate {circumflex over (P)}other(t) being an estimate thereof, and
wherein a thermal noise PN(t) expresses a sum of undesired signals present in the cell of interest at the time t other than the own cell load Pown(t) and other than the other cell interference Pother(t) and the thermal noise estimate {circumflex over (P)}N(t) being an estimate thereof.

14. The radio network node of claim 13, wherein in order to estimate the grant utilization probability pload(t1) and to estimate the interference-and-noise sum Pother(t1)+{circumflex over (P)}N(t1), the scheduler is structured to:
calculate a total scheduled grant Gown(t1−TD),
obtain a total used grant Gown(t1−TD),
measure a grant utilization





  
    
      
        
          G
          _
        
        own
      
      ⁡
      
        (
        
          
            t
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          -
          
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            D
          
        
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        own
      
      ⁡
      
        (
        
          
            t
            1
          
          -
          
            T
            D
          
        
        )
      
    
  
  ,




and
obtain the grant utilization probability estimate {circumflex over (p)}grant(t1) and the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) based on the measured grant utilization





  
    
      
        
          G
          _
        
        own
      
      ⁡
      
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          -
          
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        own
      
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wherein the total scheduled grant Gown(t−TD) expresses an amount of the radio resources granted for use by the cell terminals for uplink transmissions at the time t, and
wherein the total used grant Gown(t1−TD) expresses an amount of the radio resource grants used by the cell terminals for the uplink transmissions at the time t, and
wherein TD represents a delay between calculation of the total scheduled grant and a time the schedule takes effect on an air interface.

15. The radio network node of claim 13, wherein in order to estimate the grant utilization probability pload(t1) and to estimate the interference-and-noise sum Pother(t1)+PN(t1), the scheduler is structured to:
measure a total wideband power yRTWP(t1),
obtain the grant utilization probability estimate {circumflex over (p)}load(t1) based on the measured total wideband power yRTWP(t1), and
obtain the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) based on the measured total wideband power yRTWP(t1).

16. The radio network node of claim 15, wherein in order to obtain the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1), the scheduler is structured to:
determine a gain factor g(t1) based on the grant utilization probability estimate {circumflex over (p)}grant(t1) and the total scheduled grant Gown(t0),
model the measured total wideband power yRTWP(t1) as a combination of the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) weighted by the gain factor g(t1) and a measurement uncertainty eRTWP(t1); and
obtain the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) based on the measured total wideband power yRTWP(t1) and the model thereof.

17. The radio network node of claim 13, wherein in order to estimate the grant utilization probability pload(t1) and to estimate the interference-and-noise sum Pother(t1)+PN(t1), the scheduler is structured to:
model the grant utilization probability pgrant(t) and the interference-and-noise sum Pother(t)+PN(t) as states




  
    
      
        x
        
          1
          ,
          1
        
      
      ⁡
      
        (
        t
        )
      
    
    =
    
      
        p
        grant
      
      ⁡
      
        (
        t
        )
      
    
  




  ⋮




  
    
      
        x
        
          1
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        p
        grant
      
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          t
          -
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        )
      
    
  



and x2(t)=Pother(t)+PN(t) in a state vector x(t) of a state space model,
model a measured total wideband power yRTWP(t) and a measured grant utilization ygrantUtilization(t) in an output measurement vector y(t) of the state space model,
obtain a predicted state vector {circumflex over (x)}(t1|t0) which includes therein predicted states {circumflex over (x)}1,1(t1|t0), {circumflex over (x)}1,2(t1|t0) . . . {circumflex over (x)}1,I(t1|t0), {circumflex over (x)}1,TD/TTTI+1(t1|t0), {circumflex over (x)}2(t1|t0) whose values are based on the grant utilization probability estimate {circumflex over (p)}grant(t0) and the interference-and-noise sum estimate {circumflex over (P)}other(t0)+{circumflex over (P)}N(t0),
update the predicted state vector {circumflex over (x)}(t1|t0) based on one or more measurements included in an output measurement vector y(t1) applicable at the time t1 to obtain an estimated state vector {circumflex over (x)}(t1|t1)={circumflex over (x)}(t1), and
obtain estimated states {circumflex over (x)}1,1(t1), {circumflex over (x)}1,2(t1) . . . {circumflex over (x)}1,I(t1), {circumflex over (x)}2(t1) from the estimated state vector {circumflex over (x)}(t1) as the grant utilization probability estimate of the delay line chain, {circumflex over (x)}1,1(t1)={circumflex over (p)}grant(t1), . . . , {circumflex over (x)}1,TD/T+1(t1)={circumflex over (p)}grant(t1−TD) and the interference-and-noise sum estimate {circumflex over (x)}2(t1)={circumflex over (P)}other(t1)+{circumflex over (P)}N(t1),
wherein modeling errors and measurement errors are incorporated in the state space model as a model error vector w(t) and a measurement error vector e(t),
wherein the predicted state vector {circumflex over (x)}(t|t−T) denotes a prediction of the state vector x(t) based on information available up to a time t−T, and
wherein the estimated state vector {circumflex over (x)}(t|t)={circumflex over (x)}(t) denotes an estimate of the state vector x(t) based on information available up to the time t.

18. The radio network node of claim 17, wherein in order to update the predicted state vector {circumflex over (x)}(t1|t0), the scheduler is structured to:
model the measured total wideband power yRTWP(t1) applicable at the time t1 as





  
    
      
        y
        RTWP
      
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    =
    
      
        
          
            x
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          -
          
            
              ∑
              
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TD representing a delay between calculation of the schedule and a time the schedule takes effect on an air interface,
model the grant utilization ygrantUtilization(t1) applicable at the time t1 as ygrantUtilization(t1)=x1,1(t1)+egrantUtilization(t1),
obtain a measurement matrix C(t1) around the predicted state vector {circumflex over (x)}(t1|t0), the predicted state vector {circumflex over (x)}(t1|t0) including the predicted states {circumflex over (x)}1,1(t1|t0), {circumflex over (x)}1,2(t1|t0) . . . {circumflex over (x)}1,I(t1|t0), {circumflex over (x)}1,TD/TTTI+1(t1|t0) and {circumflex over (x)}2(t1|t0) predicted based on data up to the time t0,
obtain a Kalman gain matrix Kf(t1) based on at least the measurement matrix C(t1), the measurement error vector e(t1), and a predicted covariance matrix P(t1|t0) corresponding to the predicted state vector {circumflex over (x)}(t1|t0),
update the predicted state vector {circumflex over (x)}(t1|t0) based on at least the Kalman gain matrix Kf(t1), the output measurement vector y(t1), and the measurement vector c(x(t1)) to obtain the estimated state vector {circumflex over (x)}(t1|t1)={circumflex over (x)}(t1), the estimated state vector {circumflex over (x)}(t1) including the estimated states {circumflex over (x)}1,1(t1), {circumflex over (x)}1,2(t1) . . . {circumflex over (x)}1,I(t1), {circumflex over (x)}1,TD/TTTI+1(t1) and {circumflex over (x)}2(t1) and
update the predicted covariance matrix P(t1|t0) based on at least the Kalman gain matrix Kf(t1) and the measurement matrix C(t1) to obtain an updated covariance matrix P(t1|t1) corresponding to the estimated state vector {circumflex over (x)}(t1).

19. The radio network node of claim 18, wherein the scheduler is structured to:
determine the measurement matrix C(t1) linearized around the predicted state vector {circumflex over (x)}(t1|t0) such that





  
    C
    ⁡
    
      (
      t
      )
    
  
  =
  
    
      
        ∂
        
          c
          ⁡
          
            (
            x
            )
          
        
      
      
        ∂
        x
      
    
    ⁢
    
      |
      
        x
        =
        
          
            x
            ^
          
          ⁡
          
            (
            
              
                t
                ⁢
                
                  
                
                ⁢
                1
              
              |
              
                t
                ⁢
                
                  
                
                ⁢
                0
              
            
            )
          
        
      
    
  




to obtain the measurement matrix C(t1),
determine Kf(t1)=P(t1|t0)CT(t1)(C(t1)P(t1|t0)CT(t1)+R2(t1))−1 in which CT(t) is a transpose of the measurement matrix C(t) and (R2(t)) is a measurement covariance matrix corresponding to the measurement error vector e(t) to obtain the Kalman gain matrix Kf(t1),
determine {circumflex over (x)}(t1|t1)={circumflex over (x)}(t1|t0)+Kf(t1)(y(t1)−c({circumflex over (x)}(t1|t0))) to update the predicted state vector {circumflex over (x)}(t1|t0) to obtain the estimated state vector {circumflex over (x)}(t1|t1)={circumflex over (x)}(t1), and
determine P(t1|t1)=P(t1|t0)−Kf(t1)C(t1)P(t1|t0) to update the predicted covariance matrix P(t1|t0) to obtain the updated covariance matrix P(t1|t1).

20. The radio network node of claim 18,
wherein the scheduler is structured to project the estimated state vector {circumflex over (x)}(t1) based at least on dynamic modes corresponding to the cell of interest to obtain a predicted state vector {circumflex over (x)}(t2|t1), t2−t1=T,
wherein the predicted state vector {circumflex over (x)}(t2|t1) includes predicted states {circumflex over (x)}1,1(t2|t1), {circumflex over (x)}1,2(t2|t1) . . . {circumflex over (x)}1,I(t2|t1), {circumflex over (x)}1,TD/TTTI+1(t2|t1) and {circumflex over (x)}2(t2|t1), and
wherein the state space model is characterized through equations x(t+T)=A(t)x(t)+B(t)u(t)+w(t) and y(t)=c(x(t))+e(t), in which x(t) represents the state vector, u(t) represents an input vector, y(t) represents the output measurement vector, w(t) represents the model error vector, e(t) represents the measurement error vector, A(t) represents a system matrix describing dynamic modes of the system, B(t) represents an input gain matrix, c(x(t)) represents a measurement vector which is a function of the states of the system, t represents the time and T represents a sampling period.

21. The radio network node of claim 18, wherein the scheduler is structured to project the updated covariance matrix P(t1|t1) to obtain a predicted covariance matrix P(t2|t1) based on at least the system matrix A(t1) and a system noise covariance matrix R1(t1).

22. The radio network node of claim 21, wherein the scheduler is structured to:
determine {circumflex over (x)}(t2|t1)=A{circumflex over (x)}(t1|t1)+Bu(t1) to project the estimated state vector {circumflex over (x)}(t1) to obtain the predicted state vector {circumflex over (x)}(t2|t1), and
determine P(t2|t1)=AP(t1|t1)AT+R1(t1) in which AT is a transpose of the system matrix A(t) to project the updated covariance matrix P(t1|t1) to obtain the predicted covariance matrix P(t2|t1).

23. The radio network node of claim 13, wherein in order to estimate the other cell interference Pother(t1), the scheduler is structured to:
obtain a thermal noise floor estimate {circumflex over (N)}(t1) corresponding to the cell of interest as the thermal noise estimate {circumflex over (P)}N(t1), and
subtract the thermal noise estimate {circumflex over (P)}N(t1) from the interference-and-noise sum estimate {circumflex over (P)}other(t1)+{circumflex over (P)}N(t1) to obtain the other cell interference estimate {circumflex over (P)}other(t1).

24. The radio network node of claim 13, wherein T is equal to a transmission time interval (TTI).

25. A non-transitory computer-readable medium which has stored therein programming instructions, wherein when a computer executes the programming instructions, the computer executes a method performed in a radio network node of a wireless network for determining other cell interference applicable, wherein the method is the method of claim 1.