scholarly journals On Time-Frequency Synchronization in LoRa System: From Analysis to Near-Optimal Algorithm

2021 ◽  
Author(s):  
Vincent Savaux ◽  
Christophe Delacourt ◽  
Patrick Savelli
Keyword(s):  
Cost Function ◽  
Optimal Algorithm ◽  
A Priori ◽  
Low Complexity ◽  
Frequency Offset ◽  
Maximization Problem ◽  
Frequency Synchronization ◽  
Time Frequency ◽  
Time Offset ◽  
Ml Estimator

This paper deals with time and frequency synchronization in LoRa system based on the preamble symbols. A thorough analysis of the maximum likelihood (ML) estimator of the delay (time offset) and the frequency offset shows that the resulting cost function is not concave. As a consequence the a priori solution to the maximization problem consists in exhaustively searching over all the possible values of both the delay and the frequency offset. Furthermore, it is shown that these parameters are intertwined and therefore they must be jointly estimated, leading to an extremely complex solution. Alternatively, we show that it is possible to recover the concavity of the cost function, from which we suggest a low-complexity synchronization algorithm, whose steps are described in detail. Simulations results show that the suggested method reaches the same performance as the ML exhaustive search, while the complexity is drastically reduced, allowing for a real-time implementation of a LoRa receiver. <br>

scholarly journals On Time-Frequency Synchronization in LoRa System: From Analysis to Near-Optimal Algorithm

2021 ◽  
Author(s):  
Vincent Savaux ◽  
Christophe Delacourt ◽  
Patrick Savelli
Keyword(s):  
Cost Function ◽  
Optimal Algorithm ◽  
A Priori ◽  
Low Complexity ◽  
Frequency Offset ◽  
Maximization Problem ◽  
Frequency Synchronization ◽  
Time Frequency ◽  
Time Offset ◽  
Ml Estimator

This paper deals with time and frequency synchronization in LoRa system based on the preamble symbols. A thorough analysis of the maximum likelihood (ML) estimator of the delay (time offset) and the frequency offset shows that the resulting cost function is not concave. As a consequence the a priori solution to the maximization problem consists in exhaustively searching over all the possible values of both the delay and the frequency offset. Furthermore, it is shown that these parameters are intertwined and therefore they must be jointly estimated, leading to an extremely complex solution. Alternatively, we show that it is possible to recover the concavity of the cost function, from which we suggest a low-complexity synchronization algorithm, whose steps are described in detail. Simulations results show that the suggested method reaches the same performance as the ML exhaustive search, while the complexity is drastically reduced, allowing for a real-time implementation of a LoRa receiver. <br>

scholarly journals A distributed, plug-n-play algorithm for multi-robot applications with a priori non-computable objective functions

2019 ◽  
Vol 38 (7) ◽  
pp. 813-832 ◽  
Author(s):  
Athanasios Ch Kapoutsis ◽  
Savvas A Chatzichristofis ◽  
Elias B Kosmatopoulos
Keyword(s):  
Cost Function ◽  
Fault Tolerant ◽  
A Priori ◽  
Analytic Form ◽  
Low Complexity ◽  
General Purpose ◽  
Robot Dynamics ◽  
Adaptive Optimization ◽  
Wide Range ◽  
Multi Robot

This paper presents a distributed algorithm applicable to a wide range of practical multi-robot applications. In such multi-robot applications, the user-defined objectives of the mission can be cast as a general optimization problem, without explicit guidelines of the subtasks per different robot. Owing to the unknown environment, unknown robot dynamics, sensor nonlinearities, etc., the analytic form of the optimization cost function is not available a priori. Therefore, standard gradient-descent-like algorithms are not applicable to these problems. To tackle this, we introduce a new algorithm that carefully designs each robot’s subcost function, the optimization of which can accomplish the overall team objective. Upon this transformation, we propose a distributed methodology based on the cognitive-based adaptive optimization (CAO) algorithm, that is able to approximate the evolution of each robot’s cost function and to adequately optimize its decision variables (robot actions). The latter can be achieved by online learning only the problem-specific characteristics that affect the accomplishment of mission objectives. The overall, low-complexity algorithm can straightforwardly incorporate any kind of operational constraint, is fault tolerant, and can appropriately tackle time-varying cost functions. A cornerstone of this approach is that it shares the same convergence characteristics as those of block coordinate descent algorithms. The proposed algorithm is evaluated in three heterogeneous simulation set-ups under multiple scenarios, against both general-purpose and problem-specific algorithms.

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