Vol 62, No 12 (2019)

In this paper it is represented an efficient method for calculation of periodic stationery states of non-linear electronic circuits at time domain. The method is based on application of Kotelnikov-Shannon series for approximation of derivatives of mathematic models of the circuit. Cyclic approximation form with application of Shannon kernel allows to obtain simple matrix relation for the derivatives. The coefficients matrix in obtained expressions does not depend on amount of unknown signals in the circuit and it depends on selected amount of time samples. Amount of time samples is selected considering necessary accuracy of the result and non-linearity degree of the circuit. This method allows to convert the system of differential algebraic equations into a system of non-linear algebraic equations which can be solved by means of Newton-Raphson method, for example. In this paper there are represented several examples of calculation of stationery states of non-linear electronic circuits demonstrating the method efficiency. There are also represented the experimental results of voltage rectifier proving the represented method accuracy.

In this paper, we consider M_t×M system (M_t > M), where M_t and M are the numbers of antennas at the transmitter and receiver, respectively. We select M out of M_t transmit antennas using two different antenna selection schemes. In scheme 1, we select the subset of M antennas out of total \((\begin{array}{l}{M_{t}} \\{M}\end{array})\) subsets. In the selected subset, the minimum SNR is maximum compared to minimum SNR of all the remaining subsets. In scheme 2, M_t available transmit antennas are divided into M_tg disjoint groups of successive antennas, where M_tg = M_t/N. It means that there are N antennas in each group, where N ≤ M. Further both M_t and M are divisible by N and the total possible combinations of available groups are given \((\begin{array}{l}{M_{tg}} \\{C}\end{array})\)

Then we select the subset of M antennas out of total \((\begin{array}{l}{M_{tg}} \\{C}\end{array})\) subsets. In the selected subset, the minimum SNR is maximum compared to minimum SNR of all the remaining subsets. In this scheme, N and C are chosen to meet the requirements of M selected antennas for transmission. After antenna selection, the resulting system will be M×M. We use Minimum Mean Square Error (MMSE) Vertical Bell Laboratories Layered Space Time (VBLAST) detection at the receiver for both the antenna selection schemes. We present MIMO Symbol Error Rate (SER) versus MIMO Symbol SNR using simulations for M-QAM constellations with Rayleigh fading channels. We have compared the performance of the considered systems with prevailing high complexity schemes ML and MMSE Improved VBLAST. The considered scheme 1 with MMSE VBLAST outperforms the prevailing schemes while scheme 2 with MMSE VBLAST provides similar performance in a wide range of SNR compared to prevailing schemes. However, the number of feedback bits used in scheme 2 is less as compared to scheme 1. There is a tradeoff between the SER performance and the number of required feedback bits. As N decreases, scheme 2 performance starts moving towards the performance of scheme 1. Both the systems provide the diversity gain in the fading channel.

Two methods have been proposed for enhancing the accuracy in determining the coordinates of radio emission sources by using phase systems based on reducing the dynamic and random errors in terms of the curvature of electromagnetic wave phase front during processing the signals at inputs of linear antenna array. The reduction of dynamic errors stipulated by the limited number of terms of the Maclaurin expansion of the distance-to-source function is achieved by estimating each value of distance and bearing without use of iterative methods. The reduction of random errors occurring during the source motion is performed at the expense of preliminary estimation of values of phase difference of received signals in the process of bearing estimation and values of the difference of phase differences in determining the distance by using the least squares method in the sliding window.