WO2009147261A1

WO2009147261A1 - Method for managing computation resources which is applicable to a software-defined radio system

Info

Publication number: WO2009147261A1
Application number: PCT/ES2009/000300
Authority: WO
Inventors: Xavier REVÉS BALLESTÉ; Vuk Marojevic; Antoni Gelonch Bosch
Original assignee: Universitat Politècnica De Catalunya
Priority date: 2008-05-30
Filing date: 2009-05-28
Publication date: 2009-12-10
Also published as: ES2330604A1; ES2330604B1

Abstract

For the purpose of mapping some functions, processes or parts of an SDR application on some processors with some particular computation resources, the method involves: pre-mapping said functions on some processors; forming some nodes which form a matrix of candidate nodes, each one of which is associated with a function and a processor; pre-connecting each of the candidate nodes in one column to those in the following column; checking all of the nodes in said matrix in order to evaluate the costs thereof, including those accumulated on the possible candidate paths resulting from said pre-connection; preselecting candidate nodes and paths as a function of the accumulated costs thereof; and carrying out a final selection of nodes or final mapping on the basis of the different accumulated costs and said preselection.

Description

METHOD FOR MANAGING COMPUTATION RESOURCES APPLICABLE TO A RADIO SYSTEM DEFINED BY PROGRAM

Sector of the technique The present invention concerns a method for managing computing resources applicable to a program-defined radio system, which in general comprises mapping functions, processes or parts of an application on processors with certain computing resources, selected using cost functions, and in particular a method comprising pre-mapping said functions on processors, constituting nodes, each associated with a function and a processor, which form a matrix of pre-nodes connected through the mediation of some candidate paths, traverse all the nodes of said matrix to evaluate their costs, make a preselection of candidate paths and nodes, and finally make a final selection or mapping based on the different accumulated costs and the preselection made.

State of the prior art

Program-defined radio (Software-defined radio (SDR)) can be considered as a generalization of radio by program, or software, because it characterizes a transceiver that implements one or more signal processing blocks by software. SDR is an emerging concept that influences the design of software-defined and independent signal processing chains in relation to hardware for radio communications. It introduces flexibility in wireless systems, facilitating the dynamic passage from one radio access technology (RAT) to another or, in other words, the reallocation and reallocation of computing resources from one SDR application to another.

The SDR computing context consists mainly of heterogeneous multiprocessor platforms, be they base stations (BSs) or mobile terminals (MTs), as well as software-defined signal processing chains. Mobile terminals are very limited in terms of energy and computing resources, flexibility, and support for concurrent RAT implementations. On the contrary, the computing resources of the base stations are less limited, their energy consumption is not a limitation, and the number of concurrent RAT implementations can be as high as desired. However, the potentially large number of users and the high degrees of flexibility, modularity and reconfigurability of the platforms make the management of resources in the base stations it is equally important but more complex than in the mobile terminals.

There is a need to define a flexible software structure that acts as an interface between SDR computing resources, on the one hand, and the wireless system, represented by SDR computing requirements, on the other hand. The structure must be able, by means of the application of a corresponding method, to dynamically and efficiently map SDR applications with precedence restrictions, on some SDR platforms while satisfying the SDR computing constraints. These restrictions are, first of all, the real-time computing requirements of SDR applications, defined by the demands regarding minimum bit rate and maximum latency, and the limited computing resources of SDR platforms.

There are many contributions regarding the mapping and programming of tasks in heterogeneous multiprocessor computing platforms. These contributions are focused on a wide variety of problems in general or special purpose computing contexts. Some jointly address the problems of mapping and scheduling tasks and present optimal or lower than optimal solutions with different objectives, such as minimizing the execution time or the cost of communication processes, the objective of satisfying the response times in real time, as well as other additional or alternative objectives.

US6768901 is known to manage computer resources of a radio system defined by program, mapping functions, processes or parts

^• of an application on processors with certain computing resources, selected using cost functions. It is proposed in this document to make an abstraction of computational resources in order to use a common language of capabilities, both for what refers to the available and required resources. A specific type of abstraction is not specified, downplaying, in fact, the type of abstraction to be used. On the other hand, by the article "Modeling for the management of computing resources in SDR systems", of the XXI National Symposium of the International Scientific Union of Radio, of the same inventors of the present invention, a model of an SDR system is known based on an abstraction that takes into account its limited computational resources. Also known is the application in SDR systems of the "greedy- or g-mapping" mapping, which is an approximation of local mapping that does not require any postprocessed This is based on selecting from a grid or matrix of candidate nodes, each associated with a function and a processor, based on the results of a cost function applied to each or nodes. The g-mapping algorithm first selects a node of the first column of said matrix, after which it takes into account the cost accumulated in each of the nodes of the second column taking as origin the selected node of the first column, in base at whose cost a node of the second column is selected, and so on for the rest of the columns, so that in each step only one node is selected, which is the only one that remains active when performing the next step of selecting a node of the next column.

It seems necessary to offer an alternative to the state of the art that allows, for the same matrix of candidate nodes to be mapped, to obtain better results than the one obtained with g-mapping, thanks to considering for the selection of each node, many more possible combinations of nodes than those taken into account by the g-mapping, as well as the fact of making a series of presets prior to the final selection of nodes.

Explanation of the invention

To achieve this purpose, the present invention concerns a method for managing computing resources applicable to a program-defined radio system, of the type that comprises mapping functions, processes or parts of at least one application on processors with computing resources determined, selected using cost functions by performing the following steps: a) pre-mapping each of M functions of said application to each of N processors, thus obtaining a matrix of NxM candidate nodes, each associated with a function and a processor, b) pre-connect each of the candidate nodes belonging to a column * of said matrix with all the candidate nodes of the following column, each of said connections allowing data communication through a path candidate that includes at least one originating candidate node, one of said connections and one destination candidate node, c) applying at least one a cost function to each of the N candidate nodes of the first column of said matrix, or nodes associated with a first of said functions, obtaining the cost of each of said candidate nodes, d) apply at least one cost function to the candidate paths that include the candidate nodes of the first column in connection with at least those of the second, and calculate the cumulative cost associated with each of said candidate paths that includes at least the cost of the destination node based on previous decisions and the cost of the origin node obtained in stage c), in whole or in part, thus obtaining the cost of each of said candidate paths, and: e) preselect for each node candidate of the second column at least part of the candidate path of optimal cost that leads to said candidate node of the second column or passes through it, obtaining, respectively, N first roads or segments of preselected roads, discarding the connections that join the nodes candidates of the first column with those of the second column that are not part of said first roads or segments of preselected roads.

For a first embodiment, which will be referenced in a later section as indicative of the use of a calculation window w = 1, for which each of said candidate paths is a two-node path (or path of length 1) which includes only one of said connections, a source candidate node and a destination candidate node of two consecutive columns, the method comprises carrying out:

- said step d) to apply said cost function, which is at least one, to the candidate paths that include the candidate nodes of the first column in connection with, only, the candidate nodes of the second column, and

- said step e) to pre-select, for each candidate node destination of the second column, the candidate path of optimal cost leading to it, obtaining said first N preselected paths that start from a node of the first column and end in a node of the second column.

For said first embodiment if M = 2, the method comprises selecting the. two nodes that are part of the optimal cost path, among said first preselected paths, and therefore the processor or processors associated with each of said two nodes selected as a processor or mapped processors to execute the first function, the one associated with the node of The first column, and a second function is associated to the node of the second column. On the other hand, for a more real case where M> 3, the method comprises, for said first embodiment, perform the following steps, analogous to said stages d) and e), respectively: d ') apply at least one cost function to the candidate paths that include the candidate nodes of the second column in connection with those of the Ia third, to calculate the accumulated cost associated with each one of said candidate paths that includes at least the cost of the destination node of the third column based on preceding decisions and the cost of one of said first preselected paths in stage e), each of which includes only one node of the first column connected to one node of the second column, thus obtaining the cost of each of said candidate paths destined for a respective candidate node of the third column, and e ') preselect for each candidate node destination of the third column the candidate path of optimal cost that leads to it from an origin node of the second column, obtaining N preselected second paths, discarding the connections that join the candidate nodes of the second column with those of The third that are not part of said second preselected paths.

According to the first example of embodiment when M = 3, the method comprises selecting, from said N second preselected paths, the optimum cost, and traveling it back along the first preselected path to which it is attached, to select the three nodes that are part of said path, and therefore the processor or processors associated with each of said three nodes selected as mapped processors to execute the first function, the one associated with the node of the first column, the second function, the one associated with the node of the second column, and the third function, the one associated with the node of the third column.

If instead M> 3, the method comprises, for the first example of embodiment, perform, for each of the columns following the third column, two to two and advancing column by column, steps analogous to said stages d ^J ) and e ') to finally preselect for each candidate node destination of each additional column to the third column, the optimal cost candidate path leading to it from an origin node of the immediately preceding column, obtaining N additional preselected paths per column, discarding connections that are not part of said additional preselected paths.

Finally, for said case in which M> 3, the method comprises, for the first embodiment, select, from among the N additional preselected paths that include the nodes of the last column, the optimum cost, and travel backwards together with all the preselected paths to which it is attached, to select the M nodes that are part of said route, and therefore the processor or processors associated with each of said M selected nodes as mapped processors to execute the M functions. For a second embodiment, which will be referenced in a later section as indicative of the use of a calculation window w = 2, for which each of said candidate paths includes an origin candidate node, an intermediate candidate node and a node destination candidate, of three consecutive columns respectively, interconnected by two of said connections, that is, a three-node path, the method comprises carrying out:

- said step d) to apply at least said cost function to the candidate paths, each of which includes, interconnected by two respective connections, a candidate node originating from the first column, an intermediate candidate node from the second column and a destination candidate node of the third column, to calculate the cumulative cost of each of said candidate paths of three nodes and that of their initial segments, or path segments of two nodes that include a node of the first column and one of the Ia second, and

- said step e) to preselect, for each intermediate candidate node of the second column, only part of the candidate path of three nodes of optimal cost passing through it, said pre-selected parts being said first N path segments of two nodes.

For said second embodiment, when M> 3, the method comprises performing the following stage, analogous to said stage d): d ") applying at least one cost function to the candidate paths of three nodes that include, interconnected by two respective connections, a candidate node origin of the second column, an intermediate candidate node of the third column and a destination candidate node of the fourth column, to calculate the cumulative cost associated with each of said three-node candidate paths, which includes the minus the cost of the destination node of the fourth column based on previous decisions and the accumulated cost of One of said first road segments of two preselected nodes in stage e).

Specifically when M = 4, the method comprises, for said second embodiment, perform the following steps, after said step d "): - preselect for each intermediate candidate node of the third column, the complete candidate path of three nodes of optimal cost that passes through it and ends in a node of the fourth column, obtaining N paths of three preselected nodes, and

- select, from said N paths of three preselected nodes, the optimum cost, and travel said selected path from its intermediate node, of the third column, forward and backward along with the first segment of path of two nodes preselected in stage e) to which it is attached, to select the four nodes that are part of said path, and therefore the processor or processors associated with each of said four selected nodes as mapped processors to execute the first function, the one associated with the node of the first column, the second function, the one associated with the node of the second column, the third function, the one associated with the node of the third column, and a fourth function, the one associated with the node of the fourth column .

Alternatively, when M> 4, the method comprises, for said second embodiment, performing the following stage after said stage d "): e") preselecting, for each intermediate candidate node of the third column, only part of the candidate path of three nodes of optimal cost that passes through it and ends in a candidate node of the fourth column, obtaining N second path segments of two preselected nodes.

The method comprises carrying out, for said case where M> 4 of the second embodiment, for each of the columns following the fourth column, three to three and advancing column by column, steps analogous to said stages d ") and ") for each additional three-node path that ends in each of the following or additional columns to the fourth column, with the exception of the additional three-node path that ends in column M, to preselect for each intermediate candidate node of each path of three additional nodes, only part of the candidate path of three nodes of optimal cost that passes through it, obtaining N path segments of two additional preselected nodes for each additional column to the fourth column.

With respect to said paths of three additional nodes that end in column M, the method comprises performing the following steps (for M> 4 of the second embodiment), after said stage analogous to said stage e "):

- preselect for each intermediate candidate node of column M-1, the complete candidate path of three nodes of optimal cost that passes through it and ends in a node of column M, obtaining N paths of three preselected nodes, and - select, from among said N paths of three preselected nodes, the one of optimal cost, and traveling said selected path from its intermediate node, of column M-1, forward and backward along with all the path segments of two preselected nodes to the which is linked, to select the M nodes that are part of said path, and therefore the processor or processors associated with each of said M nodes selected as mapped processors to execute the M functions. For some additional embodiments for which w> 2, or put another way when each of said candidate paths is a path of more than three nodes, the method comprises carrying out:

- said step d) to calculate the accumulated cost of each of said candidate paths of more than three nodes and that of their initial path segments of two nodes that include a node of the first column and one of the second,

- said step e) to preselect, for each candidate node of the second column, only part of the candidate path of more than three nodes of optimal cost passing through it, said pre-selected parts being said first N path segments of two nodes, and

- Perform stages analogous to said stages described for said three-node paths, preselecting for each candidate node that occupies the second position in each path of three additional nodes ending in each of the following or additional columns to the fourth column, with the exception of the path of more than three additional nodes that ends in column M, the initial segment of two nodes of the candidate path of more than three nodes of optimal cost that passes through it, obtaining N path segments of two additional preselected nodes by each additional column to the fourth column.

The method comprises performing, for said paths of more than three additional nodes that end in column M, the following steps:

- preselect for each candidate node that occupies the second position in each path of three additional nodes that ends in column M, the complete candidate path of more than three nodes of optimal cost that passes through it and ends in a node of the column M, obtaining N paths of plus three preselected nodes, and

- select, from said N paths of more than three preselected nodes, the optimum cost, and travel said selected path from its respective node that occupies the second position on the path, forward and backward along with all segments of _* path of two preselected nodes to which it is attached, to select the M nodes that are part of said path, and therefore the processor or processors associated with each of said M selected nodes as mapped processors to execute the M functions.

As regards the aforementioned preceding decisions, they influence said cost accrued at least by what concerns the remaining resources in each node after having made such decisions or preselections. The cost functions used by the method proposed by the invention evaluate the computation cost that relates the processing requirements with the available processing resources at each moment, and the communication cost that relates the bandwidth requirements to transfer data from one process to another with the corresponding bandwidths available between the processors.

The method comprises, for an exemplary embodiment, determining said computing resources of each of said processors based on a time segment, or "time slot", of a plurality of equal time segments, of sufficient duration to ensure that each The processor is capable of executing the assigned functions or processes and of transferring data to another processor before the end of said temporary segment, thus guaranteeing the real-time processing required by SDR applications.

On the other hand, in order to work with said temporary segments, the method comprises mapping said functions to finally execute the application through an instruction segmentation process, establishing the same computation requirements for each of said temporary segments.

Brief description of the drawings The foregoing and other advantages and characteristics will be more fully understood from the following detailed description of some examples of embodiment with reference to the attached drawings, which should be taken by way of illustration and not limitation, in which:

Fig. 1 is a schematic representation of a platform model with its initially available resources (a) and an application model with its resource requirements (b), usable to apply the method proposed by the present invention;

Fig. 2 schematically shows a matrix of nodes (a, c) configured according to the proposed method, with initial nodes drawn with a continuous line under analysis according to a first part of the proposed method, for an embodiment example, as well as a table of costs (b) of said nodes;

Fig. 3 shows the same matrix (a, c) of Fig. 2, for the same example of embodiment, but for a later step, or second part of the method proposed by the invention, indicating the view (a) of the paths examined in a continuous line and the view (c) the path preselected in bold, as well as a cost table (b) indicating the cost accumulated in a first node of a second column of said matrix; Fig. 4 shows views similar to those of Fig. 3, for the same second step, but applied to a second node of said second column of the matrix, indicating the view (a) the paths examined in a continuous line and Ia view (c) the preselected path in bold; Figure 5 shows similar views to those of Figure 3, with the difference that the analysis referring to said second part of the method proposed by the invention is carried out with respect to the first node of the third column;

Fig. 6 shows similar views to those of the FIg. 4, with the difference that the analysis referring to said second part of the method proposed by the invention, is carried out with respect to the second node of the third column;

Figure 7 shows views similar to those of Figures 3 and 5, with the difference that the analysis referring to said second part of the method proposed by the invention is carried out with respect to the first node of the fourth column;

Fig. 8 shows views similar to those of Fig. 4 and 6, with the difference that the analysis referring to said second part of the method proposed by the invention is carried out with respect to the second node of the fourth column, and that in (c) no line appears in bold because no path has been preselected that leads to the second node of the fourth column due to the infinite cost of both; Fig. 9 shows in view (a) the node matrix of Figs. 2 to 7, with definitely selected nodes that are part of the path indicated by dashed arrows, as well as a view (b) indicating the final mapping represented by said selected nodes;

Fig. 10 shows views similar to those of Fig. 3 but for another example of embodiment for which paths of three nodes that pass through the gray node of the view (a) are examined, said view (a) indicating the roads examined in a continuous line and the view (c) the segment of one of said preselected roads, in bold, as well as a cost table (b) indicating the accumulated costs in each of said examined roads; the FIg. 11 shows similar views to those of Fig. 10, for the same second step, but applied to the paths that pass through the gray node of the view (a);

Figure 12 shows views similar to those of Figure 10, but where the nodes under analysis have moved one position to the right, and where in the view (c) a path has been preselected, marked in bold, full of three nodes covering the last three columns; Fig. 13 shows similar views to those of Fig. 12, but where both the paths of three examined nodes (view (a)) and the preselected (view (c)) pass through the second node of the third column; Y

Fig. 14 shows in view (a) the matrix of nodes with definitively selected nodes that are part of the path indicated by dashed arrows, for the embodiment of Figs. 10 to 13, as well as a view (b) indicating the final mapping represented by said selected nodes;

Fig. 15 is a schematic representation of a matrix of NxM nodes generated and used by the method proposed by the present invention; Fig. 16 illustrates a sequence of instructions or pseudo-codes representative of the implementation of the method proposed by the present invention for an exemplary embodiment; Y

Fig. 17 is a table containing the most important variables and expressions used in the following detailed description section of some embodiments.

Detailed description of some embodiments

In this section we will refer, with reference to the attached figures, the proposed method as "t _w- mapping" algorithm or dynamic window programming algorithm w, where w indicates the size of said window, for analysis and calculation. Although a particular mapping problem is assumed, the concepts shown are valid for any problem.

To exemplify the mapping process according to the íi _v -mapping algorithm, a simple cost function has been assumed. This consists of the sum between the cost of computing and the cost of communication. The cost of computing relates the processing requirements to the available processing resources, while the communication cost relates the bandwidth requirements (to transfer data from one process to another) with the corresponding available bandwidths between the processors. Internal bandwidths to a processor are assumed infinite, so the cost of transferring data from one process to another executed within the same processor does not imply any communication cost. To ensure proper mapping, the available resources are updated after each decision of the fw-mapping. The numbers (costs) come from this cost function, which is not specified in more detail because the objective is to exemplify the operation of the ^ -mapping; The origin of these numbers is not significant but how the algorithm behaves based on these numbers. Note that a cost infinity indicates the case of requiring more resources than are available. Therefore, finite costs represent valid mappings, while infinite costs indicate invalid (partial) mappings. For this, as for any cost function applied, the objective is to optimize (minimize in this case) the cost of mapping; The algorithm makes the corresponding decisions, which will be seen below.

For what refers to the platform and application (Available and required resources), in Fig. 1a the model of a 2-processor platform is shown, indicating the processing resources (bold numbers) and communication resources (normal numbers), and in Fig. 1b the required processing resources (bold numbers) and data transfer (normal numbers) and the application model consisting of 4 processes (modules or functions) are shown.

Operation of tw-mapping step by step:

Window w = 1:

A) Part I of the algorithm, or in other words first part of the proposed method:

In the first part, the algorithm calculates the cost of mapping the process or function f _Λ to all processors (Fig. 2a). According to the chosen cost function, mapping the fi process to the processor P ₁ costs 0.5, while mapping the process A to the processor P ₂ costs 1 (Fig. 2b). These costs are saved in the corresponding nodes (Fig. 2c).

B) Part II of the algorithm: In the second part, the frmapping examines the nodes between step 2 and step

(M-w + 1). The nodes of each step can be processed in parallel, while step (/ + 1) has to be processed after the processing of the nodes of step /. For the node (P ₁ , Z ₂ ), the paths [P ₁ P ₁ J ₂ and [P ₂ Pi] ₂ are examined (Fig. 3a). Its accumulated costs, that is the cost of the origin node plus the cost of mapping f ₂ to P ₁ and P ₂ , respectively, are calculated based on the remaining resources (Fig. 3b) to choose the one with the lowest cost that marks the way forward (Fig. 3c).

For the node (P ₂ , Z ₂ ) the paths [P ₁ P ₂ J ₂ and [P ₂ P ₂ ] ₂ are examined (Fig. 4a). Its accumulated costs, that is the cost of the origin node plus the cost of mapping f ₂ to P ₁ and P ₂ , respectively, are calculated based on the remaining resources (Fig. 3b) to choose the one with the lowest cost that marks the way forward (Fig. 4c). Once the nodes of step 2 are finished processing, the nodes of step 3 are continued. These nodes are processed in the manner equivalent to that applied to the nodes of step 2, based on the costs saved and the resources available in the nodes (Pi, faith) and (P ₂ , faith) (Fig. 5 and Fig. 6). Finally, the nodes of step 4 are processed (Fig. 7 and Fig. 8).

Cj Part III of the algorithm:

Once part II of the algorithm is finished, part IiI is continued. In this part, the _w- mapping first searches for the lowest cost node under those of step M-w + 1. In the case of mapping and _r í the example, this is the node (P ₁ U), with the cost of 2.83, opposed to the infinite cost node (P ₂ U) (Fig. 9a). Starting from this node, the rmarmapping diagram is transferred through the connections marked in bold until it reaches a node in step 1, marking the crossed nodes (Fig. 9a). This returns the final mapping according to the cost function applied and the window chosen. In this case, the solution proposes mapping U, fe and f ₄ to the Pi processor and f ₃ to P ₂ (Fig. 9b). The total cost of this mapping is 2.83, as indicated by the node (P ₁ , U) (Fig. 9a).

Window w = 2:

A) Part I of the algorithm:

It is the same as in the case of w = 1 (Fig. 2).

B) Part Il of the algorithm:

The paths have a length of w = 2. There are N ^w = 2 ² = 4 paths that are compared in each node of the part Il of the algorithm. Fig. 10 illustrates the procedure for the node (P ₁ , faith) and Fig. 11 for the node (P ₂ , faith). Note that, although the cost of the path of length 2 is used to make the decision, only the first part of the path is marked and the cost corresponding to the passage of length 1 is saved (Fig. 10c and Fig. 11c). Proceed with the 2 nodes under step 3 (see Figs. 12 and 13) in an equivalent manner, with the difference that the cost accumulated up to the nodes of the fourth column is saved or assigned to the nodes of the third column and that the entire path of length 2 is marked after having made the decision. This is due to the fact that it is the last step of part _II of the _2- mapping: M-w + 1 = 4-2 + 1 = 3.

C) Part III of the algorithm: The minimum cost node is chosen under the step (M-w + 1) = (4-2 + 1) = 3, in this case the node (P ₂ , f ₃ ). Starting from this node, the fiy-mapping diagram in both directions is traversed through the marked connections until reaching step 1 on one side and step 4 on the other (Fig. 14a). The final mapping is obtained from the traversed nodes (Fig. 14b) during this procedure.

Because in SDR systems different optimization criteria are conceived, such as the one related to satisfying real-time computing requirements in difficult conditions to satisfy, or the one related to optimizing energy consumption, the method or algorithm proposed by the present invention It is general purpose, and can execute different cost functions and be dynamically adjusted to changes in the environment of radio signals.

It will be detailed below, with reference to Figs. 15 and 16, the t _w- mapping algorithm described for a more generic embodiment example than the one described above, and generalized for M functions, N processors and NxM nodes. With reference to Fig. 15, it can be seen in the diagram of t _w- mapping that contains a matrix of NxM t-nodes. A t-node is identified as (P _ΛW , _f¡ ) and represents the mapping of an SDR function _{f¡ to the} P _ΛW processor. Any t-node in step / (column / f in the diagram _or rmapping) is connected to all nodes of step t- / + 1. The sequence of _t processors [P _{ft (0)} P ^ ₁₎ - •• P _{k (w)} ] ι identifies the path-w, a path of length w, which is associated with the t-node (P _/ ^ ₎ , /)). P _k φ ₎ is the source processor of the path-w in step (/ -1) and P _{Λ (VV)} the destination processor in step / + w-1. Therefore, [P ₁ P ₁ P _N P ₁ J ₂ represents the path of three connections or segments marked in bold in Fig. 15, and is associated with the t-node (P ₁ , f ₂ ). Table 1 of Fig. 17 contains the most important variables and expressions that appear in the present specification.

. Algorithm f _w -mapping illustrated in Figure 16 pede be divided into three parts: processing in step 1 (lines 1-2 in FIG . 16), processing in steps i = 2, 3,. .., M-w + 1 (lines 3-18 in Fig. 16), and postprocessed (lines 19-20 in Fig. 16). The _w -mapp¡ng and therefore its description does not assume a particular cost function. A) Part I: processed in step 1

The first part of the algorithm refers to the SDR fi function. For any processor P ^ ₀ ), the íw-mapping {w ≥ 1) pre-maps f- _\ a P ^ ₀₎ and stores the pre-mapping cost CT (P _{ft (0)} , f-,) in the t-node ( P ^ ₀ ), f-0 (lines 1-2 in Fig. 16). The term pre-mapping indicates that the final mapping of the SDR application is not known until all of its SDR functions have been processed, or pre-mapped. B) Part II: processed in steps 1 - 2, 3, ..., M-w + 1

The fi-mapping analyzes the N road segments, or paths of length 1, that end at the t-node {P _km , f¡). These are [P ₁ P _km ] ¡, [P ₂ P ^) I, .... and [Pw PmI (line 5 in

Ia Fig. 16). To the path of 1 [P ^ ₀ ) P _f t (i>]; Ie is assigned the weight WT [P _m P _km ] ¡(line 6 in Fig. 16) This weight represents the cost of pre-mapping the SDR function f¡ to the processor P ^ ₁₎ taking into account the preceding decisions, which are provided by the t-node origin of the path of 1 (P _k (p), / M). The fi-mapping calculates the cumulative cost CJ [P _m P _k ml = CT (P _m , f _w ) + WT [P _{fc (0)} P ^ ₁₎ ], - (bold elements of line 12 in Fig. 16) for each path of 1. The path of 1 [P _{k {Q)} * P _km \ ¡is obtained from:

/ ((O) * = P _{fc (1)} ] _f } (1)

and represents the pre-mapping decision in the t-node (P ^ ₎ , f¡). (The argmin {x} function results in the argumehto (s) leading to the minimum value of x.) The algorithm finally highlights the path of 1 [P _k (p and P / c (i)] / (line 14 , in bold, of Fig. 16) and stores its accumulated cost in the t-node (P ^, f¡) (line 15).

The _w -mapping (w> 1) analyzes the ΛT w-paths that are associated with the t-node (P _{/ c (} i ₎ , / _/ ). Any of these w-paths originates from the í node in step (/ -1), runs through (P _km , f¡), and ends at the t-node in step / + w-1. The algorithm calculates the accumulated costs due to lines 5-12 of Fig. 16. Then it solves

{/ c (0) *, (2)

which offers as a result the indices of the w-path that have the minimum accumulated cost. In the case that / <(M-w + 1), the _w -mapping (w> 1) highlights the path of

1 [P _{k (} O ₎ * P _{/ c (} i ₎ l _/ and stores the corresponding accumulated cost in the node (P _{k (1)} , f¡) (lines 13-15 in Fig. 16). Otherwise, highlight the path-w [P _m * Pm) ^p K2f -

(lines 16-18 of Fig. 16).

All nodes in step / (line 4 of Fig. 16) can be processed in parallel. Once its processing has been completed, the _{w w} mapping (w ≥ 1), that is to say the method proposed by the present invention, proceeds with the step / + 1 in the case that / <(M-w + 1) and if not, proceed with part III (line 3) in the case that i =

(M-ιo + 1).

C) Part III: postprocessed Part III of the postprocessing algorithm the pre-mapping decisions of parts I and II. The íw-mapping (w ≥ 1) first highlights the í-node in step M-w + 1 that retains the minimum cost (line 19 of Fig. 16). Starting with this node, the f- _w- mapping diagram, that is the NxM matrix, is traversed backwards (or forward and backward in the case that w> 1) along the paths of 1 highlighted, at the same time that all the t-nodes that are crossed during that route are highlighted (line 20 of Fig. 16). This offers as a result M highlighted nodes, which are finally selected to specify the proposed mapping proposed for the particular problem, the cost function and the window size chosen. The parts Il and III described indicate that Ia window w controls the level of local (vs. local global scope) decisions premapeado: _r í algorithm mapping is based on local decisions. However, it maintains N different premapped in each step, one per t-node, which results in N (partially) different mapping options (bold expressions in Fig. 16). On the other hand, the í _/ w_i-mapping algorithm examines all the possible N ^M mapped from the M functions to the N processors. Specifically, it calculates the accumulated costs of the roads- (Mi), that is to say roads of length (M-1), of all the different Λ / ^{M ~ 1} roads- (Mi) that cross the í-node (P ^ ₎ , / ₂ ) (lines 5-12 in Fig. 16) and select the lowest cost (lines 17 and 18 of Fig. 16). This is done for all the nodes in step 2 (line 4 of Fig. 16). The algorithm then highlights the node (P% ψ, Z ₂ ) (line 19 of Fig. 16) and goes back and forth through the urmapping diagram, that is, the NxM matrix of interconnected nodes, to obtain the mapping final (line 20 of Fig. 16). It is thus found through the application of the method proposed by the present invention, an optimal solution for the given problem and the cost function used.

The parameter w also controls the compromise between computing efficiency and mapping performance: the larger the size of the window w, the greater the complexity of the algorithm but the better the results of the mapping. Although, as mentioned above, the method proposed by the present invention is not limited to a particular type of cost function, for a specific embodiment, a cost function is proposed that adequately manages the resources of limited computing of SDR platforms under demanding real-time conditions, where computing resources constrain the mapping of the SDR application.

The proposed cost function is defined based on the weight or cost of the road length 1 (or simple connection) WT [P ^ M; P ^] _/ ,. This cost function represents an overlap between the cost of computing and the cost of communication, as follows:

WT [PA (M) P _m ] h = WT _comp [P ^ ₁ , P _m ] _h + WT _com [P _{ft (M)} P wh; (3a) r _{/ C} (* (/ X Λ) _{/ C} W /), Λ) _<1 . wτ _comp [P _{fc (M)} P ^] _n = ⁽⁰ '" ^{k {!)} ; (3b)

WT _com [P _{ft (W)} P _{fc (0} ] _ή = ^Jh * «'* ^« > ^J. (3c)

where \ NT _comp indicates the cost of computing, and WT _with the cost of communication.

Any t-node (P ^, f¡) stores the processing capacities C ^{(/ ((/) i} ° and the remaining bandwidths β ^{w /)} '° depending on the previous pre-mapping decisions. The cost function first calculate the pre-mapping costs in the t-nodes (P ₁ , U), (P ₂ , U), ..., and (P _N , U) using the right part of (3b). -node (P ^ o ₎ , U), the processing requirement C ₁ of the SDR U function is then subtracted from the corresponding initial processing capacity C ^ ₀₎ .

This updates the remaining processing capabilities for all t-nodes in step 1.

Before processing the path of length 1 [P _{Λ (M)} P mh, C ^m ' ^h) and B ^m ' ^h) are initialized with C ^{(/ C (M)} ' ^ft - ¹⁾ and S ^{(/ C (M )} ; ^{h ~ Λ} \ The algorithm then calculates WT [P _{Λ (M)} P _m ] _h before updating C ^ - ^h) and B ^mh) . In particular, c _h is subtracted from C _m ^mh) after calculating \ NT _comp [P _k ^ ₎ P _k ^] _h with (3b). B ^{{k {l)} ' ^h \ on the other hand, is updated dynamically, subtracting any required bandwidth b _¡h from the corresponding input in β ^{(/ íW} ' ^h) immediately after adding bj _h l {-} to WT _∞m [P / _< (/ -i) P

_/ Kolή according to (3c).

As mentioned above, the method proposed by the present invention, also referred to as a "turmapping" algorithm, is applicable for different types of modeling or abstraction of an SDR system, such as the one described by each platform based on its recusers computing or processing and communication (see Fig. 1a) and that of the SDR application depending on the resources required for processing and data transfer (see Fig. 1b).

For other exemplary embodiments, the parameters to be taken into account to model both the SDR system and the SDR application may be different or complementary to those indicated regarding the processing and communication resources. An example of carrying out the proposed method contemplates using the modeling proposed in the article "Modeling for the management of computing resources in SDR systems", of the XXI National Symposium of the International Scientific Radio Union, of the same inventors of the present invention. Data that is transmitted or received through a wireless link needs to be processed while there is data to be transmitted or received. An SDR application will be executed in general during the entire user session, although there may be periods of time in which no user data is transmitted. The fact that an SDR application can be replaced by another during a user session does not affect this continuous data processing.

Due to this, the method proposed by the present invention contemplates, for an exemplary embodiment, dividing the continuous execution into periodic executions by dividing the time of each computing resource into equidistant temporary computer segments, or "time slots", and the application SDR in stages of "pipelining".

The introduction of temporary computing segments allows identifying the computing capacity of a processor based on said temporary segments, thus generating a modeling analogous to that of the mentioned article, but incorporating the aforementioned segmentation into "time slots". This provides a basic mechanism for efficient computing resource management, while meeting the maximum latency demands of SDR applications.

The execution by process of segmentation of instructions, or "pipelined", of an SDR application establishes that, in any "time slot", all SDR functions process and propagate some part of the data. That is, the same processing and the same data transfer is repeated for each time segment in a different piece of data. This introduces some synchronization requirements that PHAL

(The "Platform and Hardware Abstraction Layer") satisfies (see article "Software radios: unifying the reconfiguration process over heterogeneous platforms," EURASIP Journal on Applied Signa! Processing, vol. 2005, no. 16, pp. 2626-2640, Sept . 2005, of

X. Revés, A. Gelonch, V. Marojevic, R. Ferrus).

The "Pipelining" also introduces the latency, which must be maintained within the radio service and the limits of dependence on QoS (Quality of service).

From the discussion made in the previous paragraphs, for the modeling of the system and SDR applications based on the aforementioned temporary segments, or "time slots", the new MOPTS units (millions of operations by "time slot") and MBPTS (mega-bits by "time slot") such as t _ts -MOPS and t _ts -Mbps, where t _ts is the duration of the "time slot". MOPTS and MBPTS synchronize the available computing resources with the management based on "time slots" and are the basic units for the referred modeling. It is proposed to define tt _s according to the following equation:

where n _ts are the number of "time slots" and L _max is the maximum permissible latency for the execution of the set of tasks of the radio application in the set of available processors, which is a function of the tolerable end-to-end delay of a radio communications link due to the service and the QoS agreement between the radio service provider and the end user. In the proposed modeling, it is assumed that t _ts is large enough to allow the (efficient) execution of any SDR function in the processing chain.

Although the description of the proposed method with reference to Figs. 15, 16 and 17, it has been done in this section by calling it a "t _w -mapping" algorithm, and using equations and instructions (which are indicated in Fig. 16), Fig. 15 is also referenced from the description of the proposed method made in the explanation section of the invention, that is to say that the matrix referred to there as a matrix of NxM nodes is, for an exemplary embodiment, the matrix illustrated in Fig. 15, including all the elements mentioned in said description made in the above mentioned section, such as the nodes of the different columns (P- ,, Í _I ) ... (PN _, fi) a (P ₁ , f _M ) --- (PN, fιw) _> as well as the different connections between nodes of two consecutive columns ([P ₁ P ₁ J ₂ - [Pi PN] ₂ - - - PN PI] ₂ - PN PN] ₂ ) - - - (PI PIIM- [PI PNIM- [PN P ₁ IM- [PN PNI _M ) ₁ that make up what in this section has been referred to as roads of length 1, or road segments when they are part of a path that runs along of more than two columns.

The references in parentheses included in all the appended claims serve as an explanatory guide for a better understanding of said claims based on Fig. 15. A person skilled in the art could introduce changes and modifications in the described embodiments without going beyond the scope of The invention as defined in the appended claims.

Claims

1.- Method for managing computing resources applicable to a program-defined radio system, of the type that includes mapping functions, processes or parts of at least one application on processors with certain computing resources, selected using cost functions by performing the following steps: a) pre-mapping each of M functions (frf _M ) of said application to each of N processors (P _I -PN), thus obtaining a matrix of NxM candidate nodes (P ^ ₀ , / _/ ), each of them associated with a function and a processor, b) pre-connect each of the candidate nodes belonging to a column of said matrix with all the candidate nodes of the following column, enabling each of said connections a data communication through a candidate path that includes at least one originating candidate node, one of said connections and a destination candidate node, c) applying at least one cost function to ca gives one of the N candidate nodes ((P ₁ , ÍI) ... (PN, fi)) of the first column of said matrix, or nodes associated with a first (f-0 of said functions, obtaining the cost of each one of said candidate nodes ((P ₁ , fi) ... (PN, fi)), d) apply at least one cost function to the candidate paths that include the candidate nodes of the first column ((P ₁ , ^) ... (PN, fi)) in connection with at least those of the second ((P ₁ , f ₂ ) ... (PN, f ₂ )), and calculate the cumulative cost associated with each of said candidate paths that include at least the cost of the destination node based on previous decisions and the cost of the origin node obtained in stage c), in whole or in part, thus obtaining the cost of each of said candidate paths, and: e) preselect for each candidate node of the second column ((P ₁ , f ₂ ) ... (PN, f ₂ )) at least part of the candidate path of optimal cost leading to said candidate node of the second column (( P ₁ , Í ₂ ) ... (PN , f ₂ )) or pass through it, obtaining, respectively, N first roads or segments of preselected roads, discarding the connections ([P ₁ Pi] ₂ ... [Pi PN] 2- - - [PN P _I ] ₂ - - - [PN PN] ₂ ) that join the candidate nodes of the first column ((P ₁ , ÍI) ... (PN, fi)) with those of the second ((P ₁ , h) - - - (P _N , h)) that are not part of said first roads or segments of preselected roads.

2. Method according to claim 1, characterized in that when each of said candidate paths is a two-node path that includes only one of said connections, a source candidate node and a destination candidate node of two consecutive columns, comprise carrying out:

- said step d) to apply said cost function, which is at least one, to the candidate paths that include the candidate nodes of the first column ((P ₁ , f-ι) ... (P _N , f, )) in connection with only the candidate nodes of the second column ((P ₁ , f ₂ ) ... (P _Nl f ₂ )), and

- said step e) to pre-select, for each candidate candidate node ((P ₁ , f ₂ ) - .. (PN, h)) of the second column, the candidate path of optimal cost that leads to it, obtaining said N first preselected paths that start from a node of the first column ((P _1, f-ι) ... (P _N, fi)) and end at a node of the second column ((P ₁ , f ₂ ). .. (PN, Í2)) -

3. Method according to claim 2, characterized in that when M = 2 comprises selecting the two nodes that are part of the optimal cost path, from said first preselected paths, and therefore the processor or processors associated with each of said two nodes selected as a processor or mapped processors to execute the first function (fi), the one associated with the node of the first column ((P ₁ , ^ ... (PN, fi)), and a second function (f ₂ ) the associated to the node of the second column ((P ₁ , Í ₂ ) ... (PN, Í ₂ )) -

4. Method according to claim 2, characterized in that when M> 3, comprises performing the following steps, analogous to said stages d) and e), respectively: d ') applying at least one cost function to the candidate paths that include the candidate nodes of the second column ((P ₁ , Í ₂ ) ... (PN, h)) in connection with those of the third column ((P ₁ , Í3) ... (PN, f ₃ )), for calculate the cumulative cost associated with each of said candidate paths that includes at least the cost of the destination node of the third column ((P _1, Í ₃ ) ... (PN _, f ₃ )) based on previous decisions and the cost of one of said first preselected paths in stage e), each of which includes only one node of the first column ((P ₁ , fi) .... (P _N , fi)) connected to one node of The second column ((Pi ₁ Í ₂ ) ... (PN, h)), thus obtaining the cost of each of said candidate paths destined for a respective candidate node of the third column ((P ₁ , f ₃ ) .. . (P _N , f ₃ )), and e ') preselect for each candidate node destination of the third column ((P ₁ , Í ₃ ) ... (PN _, f ₃ )) the candidate path of optimal cost that leads to him from a node origin of the second column ((P ₁ , f ₂ ). - (PN, k)), obtaining N seconds preselected paths, discarding the connections that join the candidate nodes of Ia second column ((P ₁ , f ₂ ) .-- (PN, f ₂ )) with those of the third ((P ₁ , f ₃ ) ... (P _N, f ₃ )) that are not part of said Second shortlisted roads.

5. Method according to claim 4, characterized in that when M = 3, it comprises selecting, from said N second preselected paths, the optimum cost, and traveling backwards together with the first preselected path to which it is attached, to select the three nodes that are part of said path, and therefore the processor or processors associated with each of said three nodes selected as mapped processors to execute the first function (fi), the one associated with the node of the first column ((P _{1 ,} f |) ... (P _Ni ^)), the second function (f ₂ ), the one associated with the node of the second column ((Pi ₁ f ₂ ) ... (P _N, h)), and a third function (f ₃ ), the one associated with the node of the third column ((P ₁ , f ₃ ) ... (P _N , f ₃ )).

6. Method according to claim 4, characterized in that when M> 3, comprises performing, for each of the columns following the third column, two to two and advancing column by column, steps analogous to said stages d ') and e ') to finally preselect for each candidate node destination of each additional column to the third column, the candidate path of optimal cost that leads to it from an origin node of the immediately preceding column, obtaining N additional preselected paths per column, discarding the connections that are not part of said additional preselected paths.

7. Method according to claim 6, characterized in that for said case in which M> 3, comprises selecting, from among the N additional preselected paths that include the nodes of the last column ((P ₁ , f _M ) ... (P _N , Í _M )) _> the one of optimal cost, and to travel it back along with all the preselected paths to which it is attached, to select the M nodes that are part of said route, and therefore the processor or processors associated to each of said M nodes selected as mapped processors to execute the M functions (f _r f _M ).

8. Method according to claim 1, characterized in that when each of said candidate paths includes an origin candidate node, an intermediate candidate node and a destination candidate node, of three consecutive columns respectively, interconnected by two of said connections, comprises carrying cape:

- said step d) to apply at least said cost function to the candidate paths, each of which includes, interconnected by two respective connections, a candidate node originating from the first column ((P ₁ , f-ι) .. . (P _N , fi)), an intermediate candidate node of the second column ((P ₁ , Í ₂ ) ... (PN, h)) and a node destination candidate of the third column ((P ₁ , Í ₃ ) ... (PN, U)), to calculate the cumulative cost of each of said three-node candidate paths and that of their initial segments, or path segments of two nodes that include a node of the first column ((P ₁ , fi) ... (PN, f-ι)) and one of the second ((Pi ₁ f ₂ ) ... (PN, h) ), and - said step e) to preselect, for each intermediate candidate node of

The second column ((P ₁ , f ₂ ) ... (P _N , h)), only part of the candidate path of three nodes of optimal cost that passes through it, said pre-selected parts being said first N two road segments of two nodes

9. Method according to claim 8, characterized in that when M> 3, comprises performing the following stage, analogous to said stage d): d ") apply at least one cost function to the candidate paths of three nodes that include, interconnected by two respective connections, a candidate node origin of the second column ((P ₁ , f ₂ ) ... (PN, f ₂ )), an intermediate candidate node of the third column ((Pi ₁ Í ₃ ) ... (PN, h)) and a candidate candidate node of the fourth column ((P ₁ , f ₄ ) ... (P _N, f ₄ )), to calculate the cumulative cost associated with each ¹ of said candidate paths of three nodes, which includes at least the cost of the destination node of the fourth column ((P ₁ , f ₄ ) ... (P _N, f ₄ )) based on previous decisions and the accumulated cost of one of said first segments of the path of two preselected nodes in stage e).

10. Method according to claim 9, characterized in that when M = 4, it comprises performing the following steps, after said step d "):

- preselect for each intermediate candidate node of the third column ((P ₁ , f ₃ ) ... (PN, h)), the complete candidate path of three nodes of optimal cost that passes through it and ends in a node of Ia fourth column ((P _1, f ₄ ) ... (P _N , f ₄ )), obtaining N paths of three preselected nodes, and

- select, from said N paths of three preselected nodes, the optimum cost, and travel said selected path from its intermediate node, from the third column ((P ₁ , Í ₃ ) ... (PN, fs)), forward and backward along with the first two-node path segment preselected in stage e) to which it is attached, to select the four nodes that are part of said path, and therefore the processor or processors associated with each of said four nodes selected as mapped processors to execute the first function (fi), the one associated with the node of the first column ((Pi ₁ fi) ... (P _Ni f,)), the second function (f ₂ ), the one associated with the node of the second column ((P ₁ , f ₂ ) ... (P _N, f ₂ )), the third function (f ₃ ), the one associated with the node of the third column ((P ₁ , f ₃ ) ... (Pi _M, fs)), and a fourth function (f ₄ ), the one associated with the node of the fourth column ((P ₁ , f ₄ ) ... (P _N, f ₄ )).

11. Method according to claim 9, characterized in that when M> 4, comprises performing the following stage after said stage d "): e") preselect, for each intermediate candidate node of the third column

((Pi ₁ Í ₃ ) - _" (PN, h)), only part of the candidate path of three nodes of optimal cost that passes through it and ends in a candidate node of the fourth column ((P _1,

Í ₄ ) ... (PN _, f ₄ )), obtaining N second path segments of two preselected nodes.

12. Method according to claim 11, characterized in that it comprises, for each of the columns following the fourth column ((P ₁ , f ₄ ) ... (P _Ni f ₄ )), three to three and advancing column a column, some stages analogous to said stages d ") and e") for each additional three-node path that ends in each of the following or additional columns to the fourth column ((P ₁ , f ₄ ) ... (P _N , f ₄ )), with the exception of the additional three-node path that ends in column M, to preselect for each intermediate candidate node of each additional three-node path, only part of the candidate path of three nodes of optimal cost that passes through it, obtaining N path segments of two additional preselected nodes for each additional column to the fourth column ((P ₁ , f ₄ ) ... (P _N , f ₄ )).

13. Method according to claim 12, characterized in that it comprises performing, for said paths of three additional nodes ending in column M, the following stages, after said stage analogous to said stage e "):

- preselect for each intermediate candidate node of column M-1 ((Pi ₁ f _M- i) ... (P _N , fιvι-i)), the complete candidate path of three nodes of optimal cost that passes through it and it ends in a node of column M ((Pi ₁ Í _I V _I ) ... (PN, fwO), obtaining N paths ^' of three preselected nodes, and - selecting, from said N paths of three preselected nodes, the of optimal cost, and travel said selected path from its intermediate node ((Pi ₁ f _M _ • i) ... (P _N, f _M - _I )), from column M-1, forward and backward together with all the path segments of two preselected nodes to which it is attached, to select the M nodes that are part of said path, and therefore the processor or processors associated with each of said M nodes selected as mapped processors to execute the M functions (frfwi) -

14. Method according to any of claims 8 to 13, characterized in that when each of said candidate paths is a path of more than three nodes, it comprises carrying out: - said step d) to calculate the accumulated cost of each of said candidate paths of more than three nodes and that of their initial path segments of two nodes that include a node of the first column ((Pi ₁ fi) ... (P _N , U)) V to one of the second ((P ₁ , f ₂ ) ... (P _N , f ₂ )),

- said step e) to preselect, for each candidate node of the second column ((P ₁ , Í ₂ ) ... (PN _, h)), only part of the candidate path of more than three nodes of optimal cost that passes through it, said pre-selected parts being said first N path segments of two nodes, and

15. Method according to claim 14, characterized in that it comprises performing, for said paths of more than three additional nodes that end in column M, the following steps:

- preselect for each candidate node that occupies the second position in each path of three additional nodes that ends in column M, the complete candidate path of more than three nodes of optimal cost that passes through it and ends in a node of the column M ((P ₁ , Í _W O-. - ÍPN, fwi)), obtaining N paths of more than three preselected nodes, and

- select, from said N paths of more than three preselected nodes, the optimum cost, and travel said selected path from its respective node that occupies the second position on the path, forward and backward along with all the path segments of two preselected nodes to which it is attached, to select the M nodes that are part of said path, and therefore the processor or processors associated with each of said M selected nodes as mapped processors to execute the M functions (f _r f _M ).

16. Method according to claim 1, characterized in that said preceding decisions influence said accumulated cost at least for what concerns the remaining resources in each node after having made said decisions.

17. Method according to any of the preceding claims, characterized in that said cost functions evaluate the computation cost that relates the processing requirements to the available processing resources, and the cost of Communication puts that it relates the bandwidth requirements to transfer data from one process to another with the corresponding bandwidths available between the processors.

18. Method according to claim 1, characterized in that it comprises determining said computing resources of each of said processors (P ₁ -

PN) based on a time segment of a plurality of equal time segments, of sufficient duration (t _ts ) to ensure that each processor (P _I -PN) is capable of executing the functions (f ₁ -f M) OR processes assigned and transferring data to another processor before the end of said time segment.

19. Method according to claim 18, characterized in that it comprises mapping said functions (frfwi) in order to finally execute the application through an instruction segmentation process, establishing the same computation requirements for each of said time segments.