SOLUTION FREQUENCY PLANNING PROBLEM

ABSTRACT

This thesis contains a brief description of the algorithm for obtaining a mathematical model of the frequency resource allocation in the form of a system of linear equations whose solution allows to distribute a dedicated frequency band between channels Satellite MESH-Network.

Keywords: frequency planning, MESH-network.

INTRODUCTION

The emergence of high-speed wireless technologies has led to the formation of a new type of networks, the so-called MESH networks, where each node can act as both a transit and an end node. At the same time, depending on the application, such networks can have a fixed topology or a dynamically changeable one. The prospect of such networks is due to the lack of cable infrastructure, which is the most expensive part of almost any project. When organizing a MESH network, a natural limitation is the frequency range in which all nodes must work together and the power of the transmitter used for interaction between them. One example of such a network is a satellite communications network.

The construction of modern satellite networks generally does not imply inter-satellite data transmission, since the main task of a communication satellite is to relay the received signal from one ground station to another, where information flows are routed. Obviously, with the development of technologies, the process of routing and switching is better placed on a communication satellite, thereby reducing the time of information delivery between the source and the addressee. Another advantage in the interaction of satellites with each other is the use of those frequency ranges that cannot be used for satellite-ground station communication, due to the peculiarities of the propagation of radio waves through various layers of the atmosphere and changing weather conditions. Interactions of this kind can also arise when a swarm of Nano satellites is sent into orbit, which must interact with each other. A natural limitation in organizing such a satellite MESH network is the frequency range in which all satellites must work together and the power of the transmitter used for interaction between satellites.

The article proposes an algorithm is proposed for obtaining a mathematical model of the frequency resource distribution with a limited transmitter power and an arbitrary location of satellites in space. A feature of the proposed algorithm is its ability to work with networks containing a large number of MESH stations, since it allows the original network to be divided into a kind of clusters, which are analyzed by the basic algorithm for allocating the frequency resource. The use of the basic algorithm without clustering leads to a sharp increase in the number of operations to obtain the final system of equations.

FORMULATION OF THE PROBLEM

Let S satellites and their coordinates in space, the coverage area of the transmitter of each satellite or the radiation power and radiation pattern, as well as the shared frequency range F.

In this algorithm, it is assumed that the number of connections for each satellite will be the same as the number of satellites in its area of operation, the limitation on the number of transmitters in this algorithm is not provided and is a further development of this algorithm.

The solution of the problem. Thus, let each satellite have T_S transmitters, then the total number of transmitters will be:

                                                                          (1)

The proposed algorithm allows you to determine the transmitters that will operate at the same frequency, thus, the entire set of transmitters T can be divided into N groups, the transmitters in the same group will operate in a certain frequency range Δf_N such that:

                                                                        (2)

If we denote by Δf_ijn the frequency of the transmitter, where i (1..S) is the number of the transmitting satellite, j (1..S) is the number of the receiving satellite, n (1..N) is the number of the group that includes this frequency range, then proceeding from all Δf_ijn having the same index n are equal to each other and equal to Δf_N, respectively. As a result, the following system of linear equations can be obtained:

                                                                     (3)

The solution to which will be such an allocation of frequency channels for each transmitter, in which the interference-free interaction of satellites with each other with simultaneous reuse of the allocated frequency range will be ensured.

Here is a short verbal description of the algorithm. Based on the initial data, it is necessary to construct a general reception-transmission matrix (hereinafter matrix A), which displays the network topology in a tabular form. From the resulting matrix A, it is necessary to temporarily exclude isolated radio stations, that is, those radio stations that do not transmit or receive signals from anyone; they will be taken into account in the subsequent allocation of radio frequencies. In the general network topology, it is possible that there are groups of radio signals that interact only within the group, and therefore it is necessary to divide the matrix A into receive-transmit submatrices (submatrix A_i), which describe the interaction of radio stations within the group. For each submatrix А_i, it is necessary to construct submatrices B_i, the construction algorithm of which is described in [1], but the construction of the submatrix B_i is carried out not for each radio transmission, but for each radio station, where, as a result, the size and elements of the submatrices А_i and B_i are the same. From each submatrix A_i, a metric submatrix (submatrix C_i) is constructed, where the minimum number of transitions from one radio station to another is indicated, for example, using the Ford-Bellman algorithm, where the submatrix A_i is taken as the weight matrix. The search for single-frequency signals is described in [1], but in disputable situations of choice, the choice is given to the radio station that has the smallest row-by-row sum in the submatrix B_i and the smallest value in the submatrix C_i. As a result, we will get a list of combinations of radio frequency signals and individual combinations of radio frequencies for each group. In each group, the combination with the highest weight is selected, where the weight means the number of radio stations included in this or that combination. The selected combinations for the groups are combined into a single combination, which is assigned one frequency value, and then combinations are selected, except for those already selected, until all the lists of combinations have exhausted the values. As a result, we get a general list of combinations, where the radio stations temporarily excluded from the matrix A are added to the combination with the highest weight. Frequency distribution is carried out according to [1], where adjustments are possible according to the characteristics of a specific task. For each radio station, we introduce a frequency extension, where an additional frequency band is assigned to the radio station. The search for an additional extension is carried out from a common matrix B, which is set according to the principle of constructing submatrices B_i, where the selected radio station should be able to be on the same frequency with all radio stations of another combination or a radio station that has an individual frequency.

CONCLUSION

The proposed algorithm allows one to determine the frequency plan of a satellite MESH network with an arbitrary topology and large dimension, since it allows one to split the original MESH network into a set of simpler networks, which can be analyzed using the basic algorithm from [1]. Having obtained the system of equations (3) and choosing various options for the values of Δf_N and based on various efficiency criteria, it is possible to obtain various options for satellite connections, thereby synthesizing the required topology for a specific task.

References:

1. Demichev, M. S. Solution of the PROBLEM of FREQUENCY PLANNING MESH NETWORKS // Scientific community of students XXI century. Engineering SCIENCE: collection of articles on the Mat. XLIV Intern. stud. scientific.-pract. Conf.