Development of a method for estimating the effect of transformation of the normalized frequency mismatch function of a coherent bundle of radio pulses on the quality of radar frequency resolution

The necessity of studying the influence of the transformation of the frequency mismatch function of a coherent bundle of radio pulses on the quality of solving the radar frequency resolution problem is substantiated. This solution determines the effectiveness of radar observation of high-speed and maneuvering individual and group aerodynamic objects. The method is based on explicit expressions for calculating the normalized frequency mismatch function of a coherent bundle of radio pulses, taking into account its transformation due to the radial motion of high-speed and maneuvering individual and group aerodynamic objects. The estimation of the potential frequency resolution of bundles with different numbers of radio pulses with typical parameters for a coherent pulse radar is carried out. Possible values of frequency resolution under the additive effect of uncorrelated internal noise of the radar receiver and the multiplicative effect of correlated phase fluctuations of the radar signal are estimated. With an insignificant multiplicative effect of correlated phase fluctuations, a twofold increase in the number of radio pulses in a bundle provides an improvement in the frequency resolution (reduction of the width of the normalized frequency mismatch function) by 100 %. With the predominant multiplicative effect of these fluctuations, a twofold increase in the number of radio pulses results in an improvement in the frequency resolution by about 40 %. The developed method is of great theoretical and practical importance for the further development of the radar theory of high-speed and maneuvering individual and group aerodynamic objects.

A Gated Oscillator Clock and Data Recovery Circuit for Nanowatt Wake-Up and Data Receivers

This article presents a data-startable baseband logic featuring a gated oscillator clock and data recovery (GO-CDR) circuit for nanowatt wake-up and data receivers (WuRxs). At each data transition, the phase misalignment between the data coming from the analog front-end (AFE) and the clock is cleared by the GO-CDR circuit, thus allowing the reception of long data streams. Any free-running frequency mismatch between the GO and the bitrate does not limit the number of receivable bits, but only the maximum number of equal consecutive bits (Nm). To overcome this limitation, the proposed system includes a frequency calibration circuit, which reduces the frequency mismatch to ±0.5%, thus enabling the WuRx to be used with different encoding techniques up to Nm = 100. A full WuRx prototype, including an always-on clockless AFE operating in subthreshold, was fabricated with STMicroelectronics 90 nm BCD technology. The WuRx is supplied with 0.6 V, and the power consumption, excluding the calibration circuit, is 12.8 nW during the rest state and 17 nW at a 1 kbps data rate. With a 1 kbps On-Off Keying (OOK) modulated input and −35 dBm of input RF power after the input matching network (IMN), a 10−3 missed detection rate with a 0 bit error tolerance is measured, transmitting 63 bit packets with the Nm ranging from 1 to 63. The total sensitivity, including the estimated IMN gain at 100 MHz and 433 MHz, is −59.8 dBm and −52.3 dBm, respectively. In comparison with an ideal CDR, the degradation of the sensitivity due to the GO-CDR is 1.25 dBm. False alarm rate measurements lasting 24 h revealed zero overall false wake-ups.

Mutual synchronization of complex structures in interacting ensembles of non-locally coupled rotators

Background and Objectives: One of the actual problems in nonlinear dynamics is the formation and interaction of complex spatial structures such as chimeras and solitary states arising in multicomponent systems. Chimera states are typical for ensembles of identical oscillators with regular, chaotic, and even stochastic behavior in a case of nonlocal interaction of the elements. They represent cluster structures, including groups of elements with synchronous and non-synchronous oscillations. Chimeras were discovered and investigated in real experiments, that indicates the possibility of observing such regimes in complex systems in living nature and in technology. Solitary states are less studied today. The regime of solitary states is characterized by the synchronous behavior of most elements of the ensemble, while individual oscillators behave in a “special state”. In the present work, an ensemble of phase oscillators with inertia (rotators) is chosen as the basic model for investigation. Such ensembles with a specific coupling topology are widely used in modeling the operation of energy networks. Ensembles of rotators with nonlocal coupling are characterized by both chimera states and solitary state regimes. The problem of interaction of ensembles of rotators with nonlocal coupling and synchronization of complex spatial structures (chimeras and solitary states) formed in them has not been studied yet. Materials and Methods: A two-layer multiplex network of rotators with a nonlocal character of intralayer interactions is considered. Each layer consists of 100 elements with the same value of the coupling coefficient and coupling phase shift for each element within one layer. The interlayer coupling is symmetric. At the initial stage, with a random choice of initial conditions, steady regimes (chimeras or solitary states) in non-interacting layers were found. Next, the interlayer coupling was introduced and the evolution of the layer dynamics in the selected initial regimes was studied. Four cases of interaction with various initial states of the layers were considered. In the first case, the two layers are completely identical and demonstrate slightly different chimera structures without interlayer coupling. Their evolution with the introduction and growth of the interlayer coupling is considered for two values of the coupling phase shift. It is shown that, starting from a certain threshold value of the interlayer coupling coefficient, the complete synchronization regime is established in the layers, and the coupling phase shift significantly affects the value of the synchronization threshold. In the second case, the previous experiment is reproduced for the two layers with a frequency mismatch. Chimera states established without interlayer interaction are characterized by significantly different average frequencies of the elements in the two layers. In the presence of non-identity of the layers (in this case, frequency mismatch), the regime of complete synchronization of spatial structures is impossible. However, with an increase in the interlayer coupling coefficient, effective synchronization can be obtained which corresponds to a slight difference in the phases of rotators in the interacting layers with full frequency synchronization. In the third case, we consider the interaction between the layers in the solitary state regimes with different spatial structures. In this case, a frequency mismatch is also introduced for the elements of the two layers. For solitary states, the effective synchronization regime with an increase in the interlayer coupling is also established. In both layers the same configurations of solitary states are realized and frequency synchronization is observed. In the fourth case, a heterogeneous multiplex network is considered, in which one layer is in the chimera state, the second layer shows the solitary state mode. With a certain strength of the interlayer coupling the complex structures are destroyed in both layers of the network and a spatially uniform regimes are established. In this case, all the rotators of the two layers rotate at the same frequency, and the difference in the regimes in the layers reduces to a small phase shift, the same for all pairs of coupled rotators of the two layers. Conclusion: The effects of synchronization in the multiplex network were established for two layers in the regimes of complex spatio-temporal dynamics, such as chimera states and solitary states. The influence of the frequency mismatch of the network elements and the phase shift in the interlayer coupling on the synchronization phenomena was studied.