The results of development a mathematical model for capacity allocation downlink technology WiMAX. The novelty of the proposed model is possible preventive limit transmission rate allocated to the service flows of the user stations in the downlink by using the WiMAX technology linear or linear-quadratic objective function. It is shown that the use of a linear-quadratic objective function in comparison with the linear, can produce a more equitable management of requests based on the relative priorities. The analysis of known methods for dividing the time-frequency resource WiMAX technology showed that they all focus on the distribution between the subscriber stations all bandwidth downlink. The model proposed is directed to the allocation of each user station a guaranteed bit rate in the absence of overload downlink as well as the preventive rate limiting allocated user stations under overload conditions. Using the mathematical model is directed to distribution between subscriber stations of a time-frequency resource of the downlink, which in turn improves the conditions in the electromagnetic frequency range used. The influence of the priority request rate used in the model, the nature of the possible failures.
Lemeshko A.V., Garkusha S.V. Model time-frequency resource allocation WiMax aimed at improving the electromagnetic compatibility // Proceeding of the 2013 IX International Conference on Antenna Theory and Techniques (ICAAT), 16-20 September, 2013, Odessa, Ukraine. - PP. 175-177.

Found that the provision of the required transmission rate of WiMAX can be achieved by solving the problem of frequency resource allocation in the downlink. As a result analyzed by the existing mechanisms of the frequency distribution of resources between subscriber stations in a downlink wireless network, operating using the technology of WiMAX. Based on the identified drawbacks of making a mathematical model the distribution of sub-channels in the network standard, IEEE 802.16, which provides a guaranteed rate subscriber stations in the downlink and submitted by a number of linear constraint equations. The novelty of the model lies in the formulation of the problem the frequency distribution of the resource allocation problem as a sub-channel with a firmly fixed number of subcarriers in each of them. The solution to the optimization problem sub-channel allocation proposed to carry out a multiple objective functions that the available frequency resources in order to allocate a minimum number of sub-channels, the distribution of the available frequency resources in order to allocate a minimum transfer speed of each the subscriber stations, the distribution of the available frequency resources to jointly minimize the number of used sub-channels and a transmission rate allocated to subscriber stations in a downlink. A comparative analysis of the solutions obtained by using different objective functions.
Al-Janabi Haider Dheyaa Kamil, Al-Dulaimi Aymen Mohammed Khodayer, Abed Ahmed Hassan Model Guaranteed Transmission Rate Providing in WiMAX Downlink // Проблеми телекомунікацій, Vol. 2013, Issue 1, 2013, pp. 3-12

Current approaches to slot allocation among data bursts in downlink of WiMAX technology were analyzed. As a result of the completed analysis drawbacks of known decisions were distinguished and basic requirements to the slot allocation problem among data bursts were formed. A mathematical model of slots allocation and data burst scheduling in the downlink of IEEE 802.16 standard is proposed. The proposed model is focused on the formation of one data packet in downlink for each subscriber station that minimizes the number of overhead information sent over the used frequency communication channel. The dependence of the amount of slots, forming one data packet from required transmission rate of a subscriber station and type of modulation and coding scheme were analyzed.
Lemeshko O., Garkusha S. Slot allocation model and data burst scheduling in downlink WiMax technology // Proceedings of IEEE XXXIII International Scientific Conference "Electronics and nanotechnology" (ELNANO), April 16-19, Kyiv, Ukraine, 2013. - PP. 455-459.

By using mathematical simulation it is carrying out analysis of advantages of using adaptable modulation of signals in MIMO channels of WiMAX systems
Loshakov Valery Andreyevich, Vadia Ziayadt Adaptive modulation of signals in MIMO channels // Проблеми телекомунікацій, Vol. 2010, Issue 1, 2010, pp. 102-108