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Model of fast conversions in Galois field and performance estimation of variant of subclass m sequences double-dwell delay acquisition


E.V. Vitomsky – Senior Lecturer, Moscow Aviation Institute (National Research University)

A delay acquisition problem of broadband signals based on code sequences with high requirements to reliability and speed of delay acquisition is considered. The problem arises in the choice of the processing method and the variant of the device implementation in order to provide a compromise between the speed and complexity of the devices due to additional limitations associated with the purpose and operating conditions of the radio systems. One of the vast classes of code sequences that makes it possible to achieve a significant simplification and speed up the search for delay are codes based on maximum length codes. The high structural redundancy of these codes is ensured by the existence subfields in the original Galois field. A useful effect of processing is achieved through the use of fast conversions in the Galois fields. One way to improve search efficiency based on fast conversions is using of the quasi-optimal solutions. Such solutions can give a gain on energy costs and complexity of multi-channel devices. A distinctive feature of fast conversions in Galois fields is the ability to process the received signal in real time, which is usually required when performing fast conversions by other methods. To confirm the merits of such search methods and devices, the actual tasks are to select the hypothesis filtering option at the first search stage and estimate the energy efficiency of the corresponding implementing schemes. A model and method to process of maximum-length codes subclass based on fast conversions in Galois fields using vector-matrix operations is developed. It can be used to obtain an effective algorithmic implementation. This is essential for various methods and algorithms analyzing, evaluating their parameters, search devices implementing. Two search models are constructed: an optimal and two-stage quasi-optimal scheme with an optimal detector in the first search stage. For these models, analytical estimates of energy efficiency were obtained. The developed search scheme version slightly complicates the structure of the device in relation to the optimal scheme. Combining the execution of the functions necessary to implement both processing steps in the same components of the device makes it possible to use the optimal method for detecting the accumulation of structural components of the long code sequence in the first search stage. The false alarm probability does not affect the accuracy of the next processing stage, and at any probability value increases energy efficiency due to reliable detection of the symbol energy accumulation at sufficiently large signal-to-noise ratios. The results of the analytical energy efficiency evaluation are obtained for the worst probability of the search time increasing due to detection circuit use. The characteristics comparison of the presented search scheme with the optimal one showed the competitiveness of two-stage schemes.

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