Due to the increased use of wireless communication technologies that enable data transmission at high speeds, unused parts of the frequency spectrum have become very limited. The regulatory bodies in charge of granting licenses for the use of certain frequency bands carry out the distribution of the rights for using the available and very limited frequency spectrum. This is the reason why the development of new and expansion of existing wireless communication systems represents a special challenge. Also, numerous studies show that insufficient flexibility in the way to access the frequency spectrum becomes a larger problem than the physical lack of spectrum resources. The concept of cognitive radio networks represents a potential solution for more efficient use of spectrum resources. This doctoral thesis deals with the problem of detecting the availability of the radio-frequency (RF) spectrum in systems with one (singe-input single-output - SISO) and multiple (multiple-input multiple-output - MIMO) transceivers on the side of primary and secondary users in OFDM cognitive radio networks. In the paper, the problem of detecting the availability of the radio frequency spectrum is analyzed using the method of primary user signal energy detection at the location of the secondary user. This method was chosen for analysis in this doctoral thesis due to its simplicity of implementation, which makes it the most widely used method of detecting RF spectrum availability in practice. The results presented in this doctoral thesis showed that the probability of reliable detection of the frequency spectrum availability is significantly influenced by the characteristics of the signal transmitted and the method of detecting this transmitted signal of the licensed (primary) user. It has been shown that the signal-to-noise ratio (SNR), the signal transmission power of the primary user, the number of antennas on the transmitter and receiver (secondary user) side, the number of samples used in the signal detection process, the influence of the variation (uncertainty) of the noise power and the set signal detection threshold, have a special influence on the reliability of the detection of the primary user's signal at the secondary user's location. Therefore, the method of detecting the signal of the primary user using the energy detection approach in SISO and MIMO OFDM systems based on the received sigla square-law combining (SLC) technique performed by the secondary user is proposed and mathematically modeled in the doctoral thesis. Based on the developed mathematical model, algorithms were also developed for carrying out the process of detecting the availability of the frequency spectrum using the method of energy detection in SISO and MIMO OFDM communication systems. Using algorithms developed in the Matlab program, an extensive simulation analysis of the probability of detection of the primary user signal was carried out, with respect to the level of the probability of a false alarm and the value of the signal-to-noise ratio (SNR) at the point of signal detection. The aforementioned interdependencies were analyzed by Matlab simulations for different values of primary user transmit powers, OFDM signal modulation techniques, number of signal samples in the signal detection process, number of transmission circuits (antennas) on the side of the primary and secondary user, uncertainties (variations) of the signal noise power and dynamic detection thresholds. The functionality of the developed algorithms was also practically tested in the process of detecting the availability of the local frequency spectrum in two different frequency spectrums using universal software-defined radio (USRP) programmed using Matlab software. The scientific contribution of the doctoral dissertation is in the development of a new method for detecting the availability of the frequency spectrum in MIMO-OFDM cognitive radio networks using the energy detection method based on the square-law combining (SLC) technique. According to the developed mathematical model, a novel algorithm was created for the computer simulation of the proposed method, which enables the reliability assessment of the new method depending on different influencing parameters in MIMO-OFDM communication systems. A model of the influence of the noise power uncertainty and dynamic detection threshold adjustment on the efficiency and reliability of detecting the available frequency spectrum using the energy detection method was developed. The developed model enables analyses of primary user energy detection reliability with respect to the impact of various influencing parameters. In particular, these parameters include different types of OFDM modulation types, signal power to noise ratio (SNR) values at the secondary user location, false alarm probabilities, numbers of transceiver circuits at the primary and secondary user sides, primary user transmit power and the number of samples used in the detection process. The analysis of the simulation results indicates an increase in the probability of detection of the primary user signal when using the method of energy detection based on the square-law combining (SLC) technique. This increase in the probability of detection spectrum availability is achieved if the process of detecting spectrum availability is carried out for a larger number of samples, a higher transmit powers of the primary user, a larger number of receiving antennas on the side of the secondary user and for higher signal power to noise ratios at the location of the secondary user. Furthermore, the simulation results indicate that different types of OFDM modulations have no influence on the reliability of the primary user's signal detection. The results achieved in the doctoral dissertation will be expanded in future research, which will be devoted to the analysis of the effectiveness of the proposed radio frequency spectrum availability detection model in massive MIMO OFDM communication systems.